Thermal aberrations are introduced into the amplified laser beam in power amplifier of a master oscillator power amplifier (MOPA) solid state laser system and degrade the beam quality. Adaptive optics (AO) system can be used to compensate for the wavefront aberrations in real time to improve the beam quality. An optimization-type adaptive optics system with the iteration rate of 100 Hz was built up. In this system,a 37-element deformable mirror is controlled by the stochastic parallel gradient descent (SPGD) algorithm with the power-in-bucket of the far-field laser beam as the metric,which is measured by a photoelectric detector. The beam cleanup experiments were performed by the SPGD AO system for the MOPA laser system comprised of Nd:YAG master oscillator and Nd:YAG power amplifier at different pumping currents. The results show that the beam quality is improved in all cases,and even for the beam with a beam quality of β>9,the β factor is decreased by 58% after cleanup. It is indicated that adaptive optics based on stochastic parallel gradient descent algorithm can be used to beam cleanup.