Private scAutoComplete As New AutoCompleteStringCollection

Private Sub bindGrid()
  DataGridView1.DataSource = getTable() ' To get Data Table for the Grid View
  setAutoComplete()
End Sub

Private Sub setAutoComplete()
   For i As Integer = 1 To 5
     scAutoComplete.Add("Praveen " & CStr(i)) ' For Sample i added my name here you can load values from database
   Next
End Sub

Private Sub DataGridView1_EditingControlShowing(ByVal sender As System.Object, ByVal e As System.Windows.Forms.DataGridViewEditingControlShowingEventArgs) Handles DataGridView1.EditingControlShowing
        If DataGridView1.CurrentCell.ColumnIndex = 1 AndAlso TypeOf e.Control Is TextBox Then ' Checking Whether the Editing Control Column Index is 1 or not if 1 Then Enabling Auto Complete Extender
            With DirectCast(e.Control, TextBox)
                .AutoCompleteCustomSource = scAutoComplete
                .AutoCompleteMode = AutoCompleteMode.SuggestAppend
                .AutoCompleteSource = AutoCompleteSource.CustomSource
            End With
        Else ' we are not Enabling Auto Complete Extendar
            With DirectCast(e.Control, TextBox)
                .AutoCompleteMode = AutoCompleteMode.None
            End With
        End If
End Sub