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

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.