arujdevia says:

dr(Gridview1.Columns(j).HeaderText) = Gridview1.Rows(1).Cells(2).Text

Set from variable i and j.

Check the updated code.

HTML

<asp:GridView ID ="gvCustomers" runat="server" AutoGenerateColumns="false">
    <Columns>
        <asp:BoundField DataField="CustomerId" HeaderText="Id" />
        <asp:BoundField DataField="Name" HeaderText="Name" />
        <asp:BoundField DataField="Country" HeaderText="Country" />
    </Columns>
</asp:GridView>
<hr />
<asp:Button ID="btnCopy" runat="server" Text="CopyOfGridView" OnClick="OnCopyOfDataTable" />
<hr />
<asp:GridView ID="gvDataTable" runat="server" AutoGenerateColumns="true"></asp:GridView>

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 (!this.IsPostBack)
    {
        this.BindGrid();
    }
}

private void BindGrid()
{
    string constring = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    using (SqlConnection con = new SqlConnection(constring))
    {
        using (SqlCommand cmd = new SqlCommand("SELECT CustomerId,Name,Country FROM Customers", con)) 
        {
            using (SqlDataAdapter sda = new SqlDataAdapter(cmd))
            {
                using (DataTable dt = new DataTable())
                {
                    sda.Fill(dt);
                    gvCustomers.DataSource = dt;
                    gvCustomers.DataBind();
                }
            }
        }
    }
}

protected void OnCopyOfDataTable(object sender, EventArgs e)
{
    DataTable dt1 = new DataTable();
    for (int j = 0; j <= gvCustomers.Columns.Count - 1; j += 1)
    {
        dt1.Columns.Add(gvCustomers.Columns[j].HeaderText);
    }
    for (int i = 0; i <= gvCustomers.Rows.Count - 1; i++)
    {
        dt1.Rows.Add();
        for (int j = 0; j <= gvCustomers.Columns.Count - 1; j += 1)
        {
            dt1.Rows[i][j] = gvCustomers.Rows[i].Cells[j].Text;
        }
    }
    gvDataTable.DataSource = dt1;
    gvDataTable.DataBind();
}

VB.Net

Protected Sub Page_Load(ByVal sender As Object, ByVal e As EventArgs) Handles Me.Load
    If Not Me.IsPostBack Then
        Me.BindGrid()
    End If
End Sub

Private Sub BindGrid()
    Dim constring As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
    Using con As SqlConnection = New SqlConnection(constring)
        Using cmd As SqlCommand = New SqlCommand("SELECT CustomerId,Name,Country FROM Customers", con)
            Using sda As SqlDataAdapter = New SqlDataAdapter(cmd)
                Using dt As DataTable = New DataTable()
                    sda.Fill(dt)
                    gvCustomers.DataSource = dt
                    gvCustomers.DataBind()
                End Using
            End Using
        End Using
    End Using
End Sub

Protected Sub OnCopyOfDataTable(ByVal sender As Object, ByVal e As EventArgs)
    Dim dt1 As DataTable = New DataTable()
    For j As Integer = 0 To gvCustomers.Columns.Count - 1 Step 1
        dt1.Columns.Add(gvCustomers.Columns(j).HeaderText)
    Next
    For i As Integer = 0 To gvCustomers.Rows.Count - 1
        dt1.Rows.Add()
        For j As Integer = 0 To gvCustomers.Columns.Count - 1 Step 1
            dt1.Rows(i)(j) = gvCustomers.Rows(i).Cells(j).Text
        Next
    Next
    gvDataTable.DataSource = dt1
    gvDataTable.DataBind()
End Sub

Screenshot