Below is the solution of my own question you can try this
<DataGrid Height="100" HorizontalAlignment="Left" Margin="12,0,0,0" Name="dataGrid2" VerticalAlignment="Top" Width="479" ItemsSource="{Binding}" TextInput="dataGrid1_TextInput" AutoGenerateColumns="False" Grid.Row="3" >
<DataGrid.Columns>
<DataGridTemplateColumn Header="Country" Width="100" >
<DataGridTemplateColumn.CellTemplate>
<DataTemplate>
<toolkit2:AutoCompleteBox Name="autoComplete" Width="300" Height="30" Margin="0" ItemsSource="{Binding lstStrState}" SelectionChanged="autoComplete_SelectionChanged"></toolkit2:AutoCompleteBox>
</DataTemplate>
</DataGridTemplateColumn.CellTemplate>
</DataGridTemplateColumn>
</DataGrid.Columns>
</DataGrid>