I would assume you are missing steps.
First, check to make sure the bearings are aligned by disconnecting the belt and sliding the Y axis back and forth by hand. It should move very freely. If there is a lot of resistance, correct your bearing alignment and make sure everything moves freely.
If everything moves without resistance, and you are still skewing, you may need to increase the current to the Y motor, or slow down your acceleration.
I would recommend a cooling fan on the motor to make sure it does not overheat and warp the plastic it is bolted to.