I'm going to stay with my girlfriend in china, do I need a Invitation Letter?

Yes, you do need her invitation and copies of her Chinese ID card or her passport and Chinese residence permit for your visa application. The invitation letter should include your travel purpose to China, your itineraries and accommodations in China, who will afford your stay in China, how long you will stay in China, her valid contacts and address in China, etc.
Besides the invitation letter, you also need to submit your passport, fill the Chin visa applicaiton form, provide a passport size photo that should be taken recently and your return air tickets.