Hii  georgeacuster...,
Please refer below sample.
HTML
<asp:GridView ID="gvCustomers" runat="server" AutoGenerateColumns="false"
    OnRowEditing="gvCustomers_RowEditing" OnDataBound="gvCustomers_DataBound" 
    OnRowCommand="gvCustomers_RowCommand">
    <Columns>
        <asp:BoundField DataField="tId" HeaderText="TId" ReadOnly="true" />
        <asp:TemplateField HeaderText="TCity">
            <ItemTemplate>
                <asp:Label ID="lblCity" runat="server"
                    Text='<%# Eval("City") %>'></asp:Label>
            </ItemTemplate>
            <EditItemTemplate>
                <asp:TextBox ID="txtCity" runat="server" TextMode="SingleLine"
                    Text='<%# Eval("City") %>'></asp:TextBox>
            </EditItemTemplate>
        </asp:TemplateField>
        <asp:TemplateField>
            <ItemTemplate>
                <asp:LinkButton ID="lnkEdit" Text="Edit" runat="server" CommandName="Edit" CommandArgument='<%# Container.DataItemIndex %>' />
            </ItemTemplate>
            <EditItemTemplate>
                <asp:LinkButton Text="Update" runat="server" OnClick="OnUpdate" />
                <asp:LinkButton Text="Cancel" runat="server" OnClick="OnCancel" />
            </EditItemTemplate>
        </asp:TemplateField>
    </Columns>
</asp:GridView>
Namespace
C#
using System.Data;
VB.Net
Imports System.Data
Code
C#
protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        this.BindGrid();
    }
}
private void BindGrid()
{
    DataTable dt = new DataTable();
    dt.Columns.AddRange(new DataColumn[2] { new DataColumn("TId"), new DataColumn("City") });
    dt.Rows.Add(1, "Mumbai");
    dt.Rows.Add(2, "San Diago");
    dt.Rows.Add(3, "Nice");
    gvCustomers.DataSource = dt;
    gvCustomers.DataBind();
}
protected void OnUpdate(object sender, EventArgs e)
{
    gvCustomers.EditIndex = -1;
    this.BindGrid();
}
protected void OnCancel(object sender, EventArgs e)
{
    gvCustomers.EditIndex = -1;
    this.BindGrid();
}
protected void gvCustomers_RowEditing(object sender, GridViewEditEventArgs e)
{
    gvCustomers.EditIndex = e.NewEditIndex;
    this.BindGrid();
}
private bool IsEditRow = false;
private int CurrentEditRowindex = -1;
   
protected void gvCustomers_DataBound(object sender, EventArgs e)
{
    if (IsEditRow && CurrentEditRowindex > -1)
    {
        for (int i = 0; i < gvCustomers.Rows.Count; i++)
        {
            if (i != CurrentEditRowindex)
            {
                gvCustomers.Rows[i].Visible = false;
            }
        }
    }
}
protected void gvCustomers_RowCommand(object sender, GridViewCommandEventArgs e)
{
    if (e.CommandName == "Edit")
    {
        IsEditRow = true;
        CurrentEditRowindex = Convert.ToInt32(e.CommandArgument);
    }
    else
    {
        IsEditRow = false;
        CurrentEditRowindex = -1;
    }
}
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 dt As DataTable = New DataTable()
    dt.Columns.AddRange(New DataColumn(1) {New DataColumn("TId"), New DataColumn("City")})
    dt.Rows.Add(1, "Mumbai")
    dt.Rows.Add(2, "San Diago")
    dt.Rows.Add(3, "Nice")
    gvCustomers.DataSource = dt
    gvCustomers.DataBind()
End Sub
Protected Sub OnUpdate(ByVal sender As Object, ByVal e As EventArgs)
    gvCustomers.EditIndex = -1
    Me.BindGrid()
End Sub
Protected Sub OnCancel(ByVal sender As Object, ByVal e As EventArgs)
    gvCustomers.EditIndex = -1
    Me.BindGrid()
End Sub
Protected Sub gvCustomers_RowEditing(ByVal sender As Object, ByVal e As GridViewEditEventArgs)
    gvCustomers.EditIndex = e.NewEditIndex
    Me.BindGrid()
End Sub
Private IsEditRow As Boolean = False
Private CurrentEditRowindex As Integer = -1
Protected Sub gvCustomers_DataBound(ByVal sender As Object, ByVal e As EventArgs)
    If IsEditRow AndAlso CurrentEditRowindex > -1 Then
        For i As Integer = 0 To gvCustomers.Rows.Count - 1
            If i <> CurrentEditRowindex Then
                gvCustomers.Rows(i).Visible = False
            End If
        Next
    End If
End Sub
Protected Sub gvCustomers_RowCommand(ByVal sender As Object, ByVal e As GridViewCommandEventArgs)
    If e.CommandName = "Edit" Then
        IsEditRow = True
        CurrentEditRowindex = Convert.ToInt32(e.CommandArgument)
    Else
        IsEditRow = False
        CurrentEditRowindex = -1
    End If
End Sub
Screenshot
