Can I do Qurban on behalf of someone who has passed on?

Yes, you can.

Many scholars from the Hanafi, Maliki and Hambali sects allow it. In accordance with what the Messenger of Allah (PBUH) did, He sacrificed two goats, the first for himself and the second for His people who have not performed Qurban. 

The sect of al-Shafi'i does not allow it.