First try a spring back pass. If you are using a live center in the tailstock, it may be the tailstock is misaligned. You can adjust the tailstock by adjusting the set screws you will find down near the base. Most tailstocks are mounted on a crossways dove tail and the set screws jack it from side to side. just put a piece of stock in and take small cuts while adjusting the tailstock back and forth untill the taper is gone. It's not rocket science!
Be carefull what you wish for, you might get it.