Aberrations will degrade trapping performance of optical tweezers. In the holographic optical tweezers, aberrations originate not only from optical elements but also from holographic phase hologram of optical traps designed by a certain algorithm. We utilize a spatial light modulator to imprint Zernike polynomials phase hologram for correcting some certain aberrations in holographic array optical tweezers which are caused by grating and lens algorithm. The results show that third-order Zernike term can effectively correct coma due to the algorithm in the optical train, and the trap stiffness for 2 μm microns diameter polystyrene beads can reach 40%. Further comparison between different Zernike term aberration correction effects demonstrates that coma caused by grating and lens algorithm in the holographic array optical tweezer has the same serious influence on tweezer trapping performance as the aberrations originating from optical elements. Meanwhile, based on first-order Zernike term aberration correction results it can be obtained that grating and lens algorithm are robust with first-order Zernike aberrations. The correcting of aberrations for algorithm in holographic optical tweezers has great significance for improving the tweezer trapping performance and deepening the understanding of specific algorithm.