Please can i apply for China Visa with my Georgia Multiple Visa in my passport.?

I am a Nigeria citizen but i live and work in Tbilisi Georgia.I want to go to China on business trip.Can i apply for the Visa here or what can i do.I have valid Georgia visa in my passport that with expiry next year 2013.Please i want to know if i can apply with this visa.because i am going for important thing for my customers.thanks.