You will have to work with a Smartlist that will display completed tasks. Then when viewing that list, select the iCal feed in that list and subscribe to it in Gcal

Thank you in advance.
I have already tried your approach, however, when I created the smartlist which display completed tasks, I cannot get the iCal feed, it just provide Atom feed.
Any idea?

The 'Events' iCal feed (which is used to show tasks as events on the calendar in Google Calendar) unfortunately doesn't include completed tasks, so I don't think this is possible right now.

Hope this helps!

One odd appraoch could be to tag your completed tasks with a completed tag, and then not mark them as complete. You could then create smart lists that excluded these tasks, and also a smart list of only completed tasks, and use that to feed the tasks onto Gcal. Might work.

I leave my task as 'uncompleted' but move them to another list when I've done the task.

This way they're not staring me the face from the inbox list and they remain in iCal.

thanks to ranbarton and n1cks, your approachs is possible and easy to implement, thanks!