Is it possible? I notice that the Gridview (Visual Studio 2010 Web Application) only contain text field and so was wonder if it is possible to convert or change a text field to a drop down list inside a Gridview.
The text field will appear if you click on the edit field and those text will be store inside a text field.

(source: microsoft.com)
You should add an edit template to your aspx.
Refer to: Walkthrough: Displaying a Drop-Down List While Editing in the GridView Web Server Control