Hi akhter,

Pls refer below code.

HTML

<asp:GridView ID="GridView1" runat="server" AutoGenerateColumns="false" OnRowDataBound="OnRowDataBound">
    <Columns>
        <asp:BoundField HeaderText="Name" DataField="ContactName" />
        <asp:TemplateField HeaderText="Country">
            <ItemTemplate>
                <asp:Label ID="lblCountry" runat="server" Text='<%# Eval("Country") %>' Visible="false" />
                <asp:DropDownList ID="ddlCountries" runat="server">
                </asp:DropDownList>
            </ItemTemplate>
        </asp:TemplateField>
    </Columns>
</asp:GridView>
<br />
<asp:Button ID="btnRefresh" runat="server" Text="Refresh" OnClick="OnRefresh" />

Namespaces

C#

using System.Data;
using System.Configuration;
using System.Data.SqlClient;

VB.Net

Imports System.Data
Imports System.Configuration
Imports System.Data.SqlClient

Code

C#

protected void Page_Load(object sender, EventArgs e)
{
    if (!IsPostBack)
    {
        GridView1.DataSource = GetData("SELECT TOP 5 ContactName, Country FROM Customers");
        GridView1.DataBind();
    }

}

private DataSet GetData(string query)
{
    string conString = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    SqlCommand cmd = new SqlCommand(query);
    using (SqlConnection con = new SqlConnection(conString))
    {
        using (SqlDataAdapter sda = new SqlDataAdapter())
        {
            cmd.Connection = con;
            sda.SelectCommand = cmd;
            using (DataSet ds = new DataSet())
            {
                sda.Fill(ds);
                return ds;
            }
        }
    }
}

protected void OnRowDataBound(object sender, GridViewRowEventArgs e)
{
    if (e.Row.RowType == DataControlRowType.DataRow)
    {
        DropDownList ddlCountries = (e.Row.FindControl("ddlCountries") as DropDownList);
        ddlCountries.DataSource = GetData("SELECT DISTINCT TOP 5 Country FROM Customers WHERE Country IS NOT NULL");
        ddlCountries.DataTextField = "Country";
        ddlCountries.DataValueField = "Country";
        ddlCountries.DataBind();
        ddlCountries.Items.Insert(0, new ListItem("Please select"));
        string country = (e.Row.FindControl("lblCountry") as Label).Text;
        if (ddlCountries.Items.FindByValue(country) != null)
        {
            ddlCountries.Items.FindByValue(country).Selected = true;
        }
    }
}

protected void OnRefresh(object sender, EventArgs e)
{
    foreach (GridViewRow row in GridView1.Rows)
    {
        DropDownList ddlCountries = (row.FindControl("ddlCountries") as DropDownList);
        ddlCountries.Items.Clear();
        // Selecting the updated record to bind the DropDownList.
        ddlCountries.DataSource = GetData("SELECT DISTINCT TOP 10 Country FROM Customers WHERE Country IS NOT NULL");
        ddlCountries.DataTextField = "Country";
        ddlCountries.DataValueField = "Country";
        ddlCountries.DataBind();
        ddlCountries.Items.Insert(0, new ListItem("Please select"));
        string country = (row.FindControl("lblCountry") as Label).Text;
        if (ddlCountries.Items.FindByValue(country) != null)
        {
            ddlCountries.Items.FindByValue(country).Selected = true;
        }
    }
}

VB.Net

Protected Sub Page_Load(ByVal sender As Object, ByVal e As EventArgs) Handles Me.Load
    If Not IsPostBack Then
        GridView1.DataSource = GetData("SELECT TOP 5 ContactName, Country FROM Customers")
        GridView1.DataBind()
    End If
End Sub

Private Function GetData(ByVal query As String) As DataSet
    Dim conString As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
    Dim cmd As SqlCommand = New SqlCommand(query)
    Using con As SqlConnection = New SqlConnection(conString)
        Using sda As SqlDataAdapter = New SqlDataAdapter()
            cmd.Connection = con
            sda.SelectCommand = cmd
            Using ds As DataSet = New DataSet()
                sda.Fill(ds)
                Return ds
            End Using
        End Using
    End Using
End Function

Protected Sub OnRowDataBound(ByVal sender As Object, ByVal e As GridViewRowEventArgs)
    If e.Row.RowType = DataControlRowType.DataRow Then
        Dim ddlCountries As DropDownList = (TryCast(e.Row.FindControl("ddlCountries"), DropDownList))
        ddlCountries.DataSource = GetData("SELECT DISTINCT TOP 5 Country FROM Customers WHERE Country IS NOT NULL")
        ddlCountries.DataTextField = "Country"
        ddlCountries.DataValueField = "Country"
        ddlCountries.DataBind()
        ddlCountries.Items.Insert(0, New ListItem("Please select"))
        Dim country As String = TryCast(e.Row.FindControl("lblCountry"), Label).Text
        If ddlCountries.Items.FindByValue(country) IsNot Nothing Then
            ddlCountries.Items.FindByValue(country).Selected = True
        End If
    End If
End Sub

Protected Sub OnRefresh(ByVal sender As Object, ByVal e As EventArgs)
    For Each row As GridViewRow In GridView1.Rows
        Dim ddlCountries As DropDownList = (TryCast(row.FindControl("ddlCountries"), DropDownList))
        ddlCountries.Items.Clear()
        ddlCountries.DataSource = GetData("SELECT DISTINCT TOP 10 Country FROM Customers WHERE Country IS NOT NULL")
        ddlCountries.DataTextField = "Country"
        ddlCountries.DataValueField = "Country"
        ddlCountries.DataBind()
        ddlCountries.Items.Insert(0, New ListItem("Please select"))
        Dim country As String = TryCast(row.FindControl("lblCountry"), Label).Text
        If ddlCountries.Items.FindByValue(country) IsNot Nothing Then
            ddlCountries.Items.FindByValue(country).Selected = True
        End If
    Next
End Sub

Screenshot