I am a US Permanent Resident(Green Card). I booked a ticket from China to USA. The flight is operated by Air Canada. It will have connecting flight wait time 11 hours 20 minutes in Vancouver. My question is that since the connecting flight wait time is so long, can I take a tour in Vancouver, I don't want to sit inside the airport, Is that possible?
Yes, you can leave the airport. Green card holders don't need a visa to visit Canada. You will need to go through Canadian immigration after arrival to Vancouver, no matter whether you decide to leave the airport or not. You should arrive at the airport in advance since you will need to clear the US immigration in Vancouver before the departure.
Update: If anybody can suggest how to spend time in Vancouver, please post a separate answer. But clearly if you take a cab to the city and back, you'll have at least 5-6 hours in Vancouver.
I'd suggest taking the Skytrain into town (perhaps Waterfront station) where you can walk around, have a nice meal, see the water, etc. If it will be summer time, you could even walk to a nearby beach. On the other hand, if you think you may be exhausted from the flight, you could book a day rate at a hotel near the airport and have a shower and nap and change of clothes.