how to display GridView row value in DropDownList using jQuery

Yes Aashish682 the code you shared works but be sure you assign different id for the dropdownlist which is present in edit dialog popup so that it wont assign same selected values to all the dropdownlist present in gridview.

<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.7.2/jquery.min.js"></script>
       <script src="http://ajax.aspnetcdn.com/ajax/jquery.ui/1.8.9/jquery-ui.js" type="text/javascript"></script>
       <link href="http://ajax.aspnetcdn.com/ajax/jquery.ui/1.8.9/themes/start/jquery-ui.css"
        rel="stylesheet" type="text/css" />

<script type="text/javascript">
      $(function () {
              $("#modal_dialog").dialog({
                  title: "CAB Details",
                  autoOpen: false,
                  width: 580,
                  open: function () {
                      $('#disableBackGround').attr('style', 'display:block');
                  },
                  buttons: {
                      ADD: function () {
                          var textvalue = $("#<%=DropDownList1.ClientID%>").val();
                          $('#<%= hndtxt.ClientID %>').val(textvalue);
                          var textvalue = $("#<%=TextBox3.ClientID%>").val();
                          $('#<%= Hiddenfield1.ClientID %>').val(textvalue);
                          var textvalue = $("#<%=DropDownList3.ClientID%>").val();
                          $('#<%= Hiddenfield2.ClientID %>').val(textvalue);
                          var textvalue = $("#<%=TextBox5.ClientID%>").val();
                          $('#<%= Hiddenfield3.ClientID %>').val(textvalue);
                          var textvalue = $("#<%=TextBox6.ClientID%>").val();
                          $('#<%= Hiddenfield4.ClientID %>').val(textvalue);
                          var textvalue = $("#<%=TextBox7.ClientID%>").val();
                          $('#<%= Hiddenfield5.ClientID %>').val(textvalue);
                          var textvalue = $("#<%=TextBox8.ClientID%>").val();
                          $('#<%= Hiddenfield6.ClientID %>').val(textvalue);
                          var textvalue = $("#<%=TextBox9.ClientID%>").val();
                          $('#<%= Hiddenfield7.ClientID %>').val(textvalue);
                          var textvalue = $("#<%=TextBox10.ClientID%>").val();
                          $('#<%= Hiddenfield8.ClientID %>').val(textvalue);
                          var textvalue = $("#<%=TextBox11.ClientID%>").val();
                          $('#<%= Hiddenfield9.ClientID %>').val(textvalue);
                          $("[id*=add]").click();
                      },
                      Close: function () {
                          $('#disableBackGround').attr('style', 'display:none');
                          $(this).dialog('close');
                      }
                  }
              });
              $("[id*=btnadd]").live("click", function () {
                  $("#modal_dialog").dialog('open');
                  $(".ui-dialog-titlebar-close").hide();
                  return false;
          });
      });
    </script>
     <script type="text/javascript">
         $(function () {
             $("#dialog").dialog({
                 title: "CAB Details",
                 autoOpen: false,
                 width: 580,
                 open: function () {
                     $('#disableBackGround1').attr('style', 'display:block');
                 },
                 buttons: {
                     Update: function () {
                         var textvalue = $("#<%=TextBox12.ClientID%>").val();
                         $('#<%= hndtxt.ClientID %>').val(textvalue);
                         var textvalue = $("#<%=DropDownList2.ClientID%>").val();
                         $('#<%= Hiddenfield1.ClientID %>').val(textvalue);
                         var textvalue = $("#<%=TextBox14.ClientID%>").val();
                         $('#<%= Hiddenfield2.ClientID %>').val(textvalue);
                         var textvalue = $("#<%=DropDownList4.ClientID%>").val();
                         $('#<%= Hiddenfield3.ClientID %>').val(textvalue);
                         var textvalue = $("#<%=TextBox16.ClientID%>").val();
                         $('#<%= Hiddenfield4.ClientID %>').val(textvalue);
                         var textvalue = $("#<%=TextBox17.ClientID%>").val();
                         $('#<%= Hiddenfield5.ClientID %>').val(textvalue);
                         var textvalue = $("#<%=TextBox18.ClientID%>").val();
                         $('#<%= Hiddenfield6.ClientID %>').val(textvalue);
                         var textvalue = $("#<%=TextBox19.ClientID%>").val();
                         $('#<%= Hiddenfield7.ClientID %>').val(textvalue);
                         var textvalue = $("#<%=TextBox20.ClientID%>").val();
                         $('#<%= Hiddenfield8.ClientID %>').val(textvalue);
                         var textvalue = $("#<%=TextBox21.ClientID%>").val();
                         $('#<%= Hiddenfield9.ClientID %>').val(textvalue);
                         var textvalue = $("#<%=TextBox22.ClientID%>").val();
                         $('#<%= Hiddenfield10.ClientID %>').val(textvalue);
                         $("[id*=Update]").click();
                     },
                     Close: function () {
                         $('#disableBackGround1').attr('style', 'display:none');
                         $(this).dialog('close');
                     }
                 }
             });
             $("[id*=Button1]").live("click", function () {
                 var row = $(this).closest('tr');
                 var ID = row.find("td:first").text();
                 $("#<%=TextBox12.ClientID%>").val(ID);
                 var Type = row.find("td:nth-child(2)").text();
                 $("#<%=DropDownList2.ClientID%>").val(Type);
                 var Cab_color = row.find("td:nth-child(3)").text();
                 $("#<%=TextBox14.ClientID%>").val(Cab_color);
                 var DriverID = row.find("td:nth-child(12)").text();
                 $("#<%=DropDownList4.ClientID%>").val(DriverID);
                 var Reg_no = row.find("td:nth-child(5)").text();
                 $("#<%=TextBox16.ClientID%>").val(Reg_no);
                 var Insurance_details = row.find("td:nth-child(6)").text();
                 $("#<%=TextBox17.ClientID%>").val(Insurance_details);
                 var FC_details = row.find("td:nth-child(7)").text();
                 $("#<%=TextBox18.ClientID%>").val(FC_details);
                 var Ownername = row.find("td:nth-child(8)").text();
                 $("#<%=TextBox19.ClientID%>").val(Ownername);
                 var Owner_mob = row.find("td:nth-child(9)").text();
                 $("#<%=TextBox20.ClientID%>").val(Owner_mob);
                 var Address = row.find("td:nth-child(10)").text();
                 $("#<%=TextBox21.ClientID%>").val(Address);
                 var Daily_start = row.find("td:nth-child(11)").text();
                 $("#<%=TextBox22.ClientID%>").val(Daily_start);
                 $("#dialog").dialog('open');
                 $(".ui-dialog-titlebar-close").hide();
                 return false;
             });
         });  
    </script>

Aashish682 says:

var DriverID = row.find("td:nth-child(12)").text();

                 $("#<%=DropDownList4.ClientID%>").val(DriverID);

 this is right code just cross check by debugging whether you are getting proper DriverID if yes then you might not be having any issue.