By default a DataGridViewComboBoxCell does not support typing into the cell. There are reasons though that typing into the combo box works well for your application. To enable this, two things have to be done. First the DropDownStyle property of the ComboBox editing control needs to be set to DropDown to enable typing in the combo box. The second thing that needs to be done is to ensure that the value that the user typed into the cell is added to the combo box items collection. This is due to the requirement that a combo box cells value must be in the items collection or else a DataError event is raised. The appropriate place to add the value to the items collection is in the CellValidating event handler.

private void dataGridView1_CellValidating(object sender,
    DataGridViewCellValidatingEventArgs e)
{
  if (e.ColumnIndex == comboBoxColumn.DisplayIndex)
  {
    if (!this.comboBoxColumn.Items.Contains(e.FormattedValue))
    {
      this.comboBoxColumn.Items.Add(e.FormattedValue);
    }
  }
}
private void dataGridView1_EditingControlShowing(object sender,
    DataGridViewEditingControlShowingEventArgs e)
{
  if (this.dataGridView1.CurrentCellAddress.X == comboBoxColumn.DisplayIndex)
  {
    ComboBox cb = e.Control as ComboBox;
    if (cb != null)
    {
      cb.DropDownStyle = ComboBoxStyle.DropDown;
    }
  }
}