Refer this code
HTML
<asp:TextBox ID="txtName" runat="server" onblur="AddNames(this);" />
<hr />
<asp:DropDownList ID="ddlNames" runat="server">
<asp:ListItem Text="Azim" Value="A"></asp:ListItem>
</asp:DropDownList>
Script
<script type="text/javascript">
function AddNames(txt) {
var option = document.createElement("option");
option.text = txt.value;
option.value = txt.value;
document.getElementById("<%=ddlNames.ClientID %>").options.add(option);
}
</script>
With Demo
<html xmlns="http://www.w3.org/1999/xhtml">
<head id="Head1" runat="server">
<title></title>
<script type="text/javascript">
function AddNames(txt) {
var option = document.createElement("option");
option.text = txt.value;
option.value = txt.value;
document.getElementById("sNames").options.add(option);
}
</script>
</head>
<body>
<form id="form1" runat="server">
<div>
<input type="text" name="name" value=" " onblur="AddNames(this);" />
<hr />
<select id="sNames">
</select>
</div>
</form>
</body>
</html>
Demo
