Validate Multiple Select ListBox using jQuery in ASP.Net

I think you don't understand the working of ListBox. In ListBox you must select item by clicking then only it is considered as selected.

Just adding items to ListBox does not mean that you have selected values.

Check this example

 <link href="ValidationEngine.css" rel="stylesheet" type="text/css" />
    <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
    <script type="text/javascript" src="http://cdn.ucb.org.br/Scripts/formValidator/js/languages/jquery.validationEngine-en.js"
        charset="utf-8"></script>
    <script type="text/javascript" src="http://cdn.ucb.org.br/Scripts/formValidator/js/jquery.validationEngine.js"
        charset="utf-8"></script>
    <script type="text/javascript">
        $(function () {
            $("#form1").validationEngine('attach', { promptPosition: "centerRight" });
            $("[id*=btnAdd]").bind("click", function () {
                $("[id*=lstFruits]").append("<option value = '1'>Mango</option>");
                $("[id*=lstFruits] option").attr("selected", "selected");
                return false;
            });
        });
    </script>
    <form id="form1" runat="server" style="padding-left: 100px">
    Please select one option?
    <br />
    <br />
    <div id="form">
        <asp:ListBox ID="lstFruits" runat="server" CssClass="validate[required]">
        </asp:ListBox>
    </div>
    <asp:Button ID="btnAdd" Text="Add Item" runat="server" />
    <asp:Button ID="Button1" Text="Submit" runat="server" />
    </form>