<div>
        <asp:TextBox ID="txtName" runat="server"></asp:TextBox> 
        <asp:RequiredFieldValidator ID="Req21" runat="server" ErrorMessage="Enter some value" Display="Dynamic" ControlToValidate="txtName"></asp:RequiredFieldValidator>
        <asp:Button ID="btnAdd" runat="server" Text="Add" onclick="btnAdd_Click" />
        <asp:GridView ID="GridView1" runat="server" AllowPaging="false" 
            AutoGenerateColumns="false" onrowdeleting="GridView1_RowDeleting">
            <Columns>
                <asp:TemplateField Visible="false">
                    <ItemTemplate>
                        <asp:Label ID="lblId" runat="server" Text='<%# Eval("Id") %>'></asp:Label>
                    </ItemTemplate>
                </asp:TemplateField>
                <asp:TemplateField HeaderText="Name">
                    <ItemTemplate>
                        <%# Eval("Name") %>
                    </ItemTemplate>
                </asp:TemplateField>
                <asp:CommandField  ShowDeleteButton="true" DeleteText="Delete" HeaderText="Delete" />
            </Columns>
        </asp:GridView>
    </div>

protected void btnAdd_Click(object sender, EventArgs e)
    {
        try
        {
            GridView1.DataSource = BuildTable(txtName.Text.Trim());
            GridView1.DataBind();
        }
        catch (Exception ex)
        {
            Response.Write(ex.Message);
        }
    }

    private DataTable getTableStructure()
    {
        DataTable dtReturn = null;
        try
        {
            dtReturn = new DataTable();
            dtReturn.Columns.Add("Id", typeof(int));
            dtReturn.Columns.Add("Name", typeof(string));
            return dtReturn;
        }
        catch (NullReferenceException)
        {
            throw;
        }
        finally
        {
            if (dtReturn != null) dtReturn = null;
        }
    }

    private DataTable BuildTable(string Value)
    {
        DataTable dtTable = null;
        try
        {
            if (Session["GridView"] == null)
                dtTable = getTableStructure();
            else
                dtTable = (DataTable)Session["GridView"];
            DataRow drNewRow = null;
            drNewRow = dtTable.NewRow();
            drNewRow[0] = dtTable.Rows.Count + 1;
            drNewRow[1] = Value;
            dtTable.Rows.Add(drNewRow);
            drNewRow = null;
            Session["GridView"] = null;
            Session["GridView"] = dtTable;
            return dtTable;
        }
        catch (NullReferenceException)
        {
            throw;
        }
    }
    protected void GridView1_RowDeleting(object sender, GridViewDeleteEventArgs e)
    {
        try
        {
            DataTable dtData = (DataTable)Session["GridView"];
            int ColumnId = Convert.ToInt32(((Label)GridView1.Rows[e.RowIndex].FindControl("lblId")).Text);
            DataRow[] drRemove = dtData.Select("Id=" + ColumnId);
            foreach (DataRow dr in drRemove)
                dtData.Rows.Remove(dr);
            Session["GridView"] = null;
            Session["GridView"] = dtData;
            GridView1.DataSource = dtData;
            GridView1.DataBind();
        }
        catch (Exception ex)
        {
            Response.Write(ex.Message);
        }
    }