I am wondering if it is possible to have a modal dialog (like JQuery) by clicking Edit button on a asp.net built in gridview control. If yes, can anymore point me out the brief process of how it could be done. Please see the picture below for clarification.
Thanks.

I see few ways to do that:
Using
OnEditCommandproperty (assuming you are using<asp:EditCommandColumnto draw that edit link):You can show popup using serverside handler (for instance, popup included into ajaxcontroltoolkit.dll which allows to show popup from serverside easily on page reload)
Another option:
Make your own column with edit link for each item. It can have OnClientClick handler which will open jQuery popup directly on client (but you will need to get row info for current line from server somehow: with your own ajax call or, suppose it will be better, using webservice with webmethod)
Second option could be modified: instead of creating own column, you may add click even handler with that same jquery on default edit link with return false, so it will prevent form submition.
I never did something like this personally and even newer saw implementations of such thing, but I would select some option from those listed above. I do not think that there is some really simply, built in way of doing that.
UPD:
Here is an example of opening popup with own edit button and modalpopupextender from ajax control toolkit (similar like in my first option except that they are using own edit button, which I think could be easily replaced by default one and OnEditCommand even handler) :
http://www.c-sharpcorner.com/UploadFile/krishnasarala/edit-gridview-row-with-model-popup-extender-in-Asp-Net-ajax/