Hi  geetasks,

You can use $('#HiddenField1').val(Name) to get the value in the TextBox and then loop through the GridView to compare it with the value in the HiddenField.

The code:

<script type="text/javascript">   

        $(document).ready(function () {
            $('#txtName').blur(function () {
                var Name = $('#txtName').val();
                $('#HiddenField1').val(Name);          
                var a =1;
                $("#<%=GridView1.ClientID%> tr td").each(function () {
                    if ($('#HiddenField1').val() == $(this).text()) {
                        alert("duplicate value")
                        a = 2;
                    }
                })
                if (a = 1) {
                    $('#Button1').click(function () {
                        $.ajax({
                            type: 'POST',
                            contentType: "application/json; charset=utf-8",
                            url: 'WebForm99.aspx/Insert_Data',
                            data: "{'Name':'" + Name + "'}",
                            async: false,
                            success: function () {
                                $("#GridView1 tbody").append("<tr><td>" + $('#txtName').val() + "</td></tr>")
                                $('#txtName').val("");
                            },
                           
                        });
                    })
                }
            });
        });

    </script>
<div>
            <asp:TextBox ID="txtName" runat="server"></asp:TextBox>
            <asp:HiddenField ID="HiddenField1" runat="server"/>
            <hr />
            <asp:GridView ID="GridView1" runat="server" AutoGenerateColumns="False" DataSourceID="SqlDataSource1">
                <Columns>
                    <asp:BoundField DataField="Name" HeaderText="Name" SortExpression="Name" />
                </Columns>
            </asp:GridView>
            <input type="button" id="Button1" value="Save" />
            <asp:SqlDataSource ID="SqlDataSource1" runat="server" ConnectionString="<%$ ConnectionStrings:CaseTestConnectionString %>" SelectCommand="SELECT [Name] FROM [Test14]"></asp:SqlDataSource>
        </div>

Aspx.cs:
[WebMethod]
        public static void Insert_Data(string Name)
        {
            SqlConnection conn = new SqlConnection(ConfigurationManager.ConnectionStrings["constr527"].ConnectionString);
            conn.Open();
            SqlCommand cmd = new SqlCommand("Insert into Test14 (Name) values(@Name)", conn);
            cmd.Parameters.AddWithValue("@Name", Name);
            cmd.ExecuteNonQuery();
            conn.Close();
        }

The result:

Best regards,

Sam