I intend to visit China for more than 30 days but L type is valid for 30 days only.

Yes, it is possible for you to do that. You can apply for the extension at the exit and entry administration of the local PSB.
You should first prepare passport, a fully filled-out application form, a passport-style photo, valid registration form of temporary residence, the return ticket and accommodation arrangement. Next, go to the exit and entry administration to submit the application.