I am US permanent resident, do I need to get a visa to Europe?
I have my passport.
Thanks in advance.

Tourist travel doesn't always require a Visa. I found this site that seems to be a good central source for info:

Travel Document Systems; Europe Page (http://www.traveldocs.com/europe.htm)

But my passport is not US passport

That page should still help

Thank you very much, but does that mean they will approve my case for sure?
If it takes a period and after that u still not sure if they allow u to go visit their country, what am I going to do with the airline tickets?
I know I can cancle it, but I prefer not...
Thank you again.

That I can't answer. That's up to the country. I can say that most countries want tourists so unles there is some reason to refuse you, they probably won't.