Adaptive optics can be used to compensate wave-front aberrations of output beam from high-power laser system for improving beam quality. To investigate the feasibility of adaptive optics method based on the stochastic parallel gradient descent (SPGD) for beam cleanup, a SPGD adaptive optics system with iterative rate of 100 Hz is built up, in which a high-speed photodetector is used as the measurement device of the system′s performance evaluation function, and a high-speed deformable mirror is served as the wave-front corrector. Dynamic wave-front aberrations caused by the heat flow turbulence of a resistance coil, are corrected in-real-time by the SPGD adaptive optics system. The experimental results show that the above-mentioned system can correct dynamic wave-front aberrations changing in the frequency range of 4 Hz below, resulting in both a 2.2-fold increase of the energy and a 1.4-fold increase of the stability of the far-field spot in the pinhole. It is indicated that the SPGD adaptive optics method is feasible for beam cleanup system.