No matter what exercise you do, you can't make fat disappear from a specific area. If you lower your fat percentage in general then the fat on your back will eventually go. Buy yourself a set of scales that measure body fat as well weight. This will help you to keep track of your fat percentage as it changes, something that may not be visible to the naked eye.

If you're talking about fat on your lower back, try this exercise recommended by trainer Matt Roberts. Lie on your back with your right leg flat on the floor and the left leg bent with your foot by your right knee. Put your right hand behind your head with your elbow level with your ear. Bring your right shoulder diagonally up towards your left knee and your left knee up towards your right shoulder. Lower. Do 15 on each side. Do three sets. Remember to breathe out as you come up and in as you come down. Works the stomach and the bottom of your back at the same time! For upper back, ask your gym instructor to show you how to use the lateral pulldown machine. Or learn to do chin ups - it'll make you feel like Lara Croft while giving you a back to be proud of.

Draw your legs to the breast and roll forwards and let fall back afterwards again. it will exercise your back and will give you a wonderful massage :D Try it!

Arms at your sides and push backwards quickly. Repeat 20 times. It really works.