Hi guys, I am working on BLDC drive and use A3931 Allegro make IC it's working fine in Forward direction but in reverse direction it's giving 60% RPM,So anybody give explanation or idea about it.

Hi, I don't know exactly your control circuit. But I would check the correct triggering angle of the hall sensors first. It is good if you have a small amount of advanced angle (effect of mechanical position and also hall histeresis) but this becomes negative if you change the motor direction.
Another possibility in speed change is if your control changes from trapezoidal to sinewave. I worked with some control chips that could'n do sinewave control in reverse direction.

That chip is obsolete - but you probably know that.
Try testing the hall alignment to the motor - rotate it in the opposite direction of the high speed by about 5 degrees and retest.