A beam cleanup subsystem is usually contained in high power laser system to correct for the wavefront aberrations of the output beam of the laser resonator continuously. To investigate the feasibility of the stochastic parallel gradient descent (SPGD) adaptive optics method on beam cleanup issue, dynamical wavefront aberrations, analogous to the commonly encountered wavefront distortions in high power laser beams, are first introduced into the experimental laser beam by continuously changing the surface shape of a 37-element deformable mirror incorporated in the system according to the iteration sequence of the SPGD algorithm, and then the same deformable mirror is used to correct for the produced aberrations by applying the SPGD algorithm to upgrade the control voltages of the mirror actuators. The experimental results show that, when the initial aberrations of the system being removed, the dynamic wavefront aberrations of the laser beam can be compensated successfully and the beam quality remains on a high level during the whole correction period with the system working on simulated iteration rates of 1 kHz and 2 kHz respectively. It is indicated that the SPGD adaptive optics method is feasible on beam cleanup system.