The correction ability of dynamic phase error in coherent beam combination for multi-channel large solid laser device is analyzed by stochastic parallel gradient descent (SPGD) algorithm. The fundamental theory of coherent beam combination by SPGD algorithm is introduced. The algorithm is optimized by numerical simulation method. Coherent beam combination of two beams with the wavelength of 800 nm and the bandwidth of 30 fs is experimentally achieved and the performances of SPGD algorithm under the 10, 15, 20, 25 Hz dynamic phase error conditions are tested. Moreover, the processes of dynamic piston and point phase error correction are simulated. The influence of phase noises with different intensities and frequencies on the correction ability is analyzed. The relationships among the control bandwidth, number of beams and iteration rate are computed. The results show that the quadratic sum of far-field intensity is the optimal performance evaluation function of coherent beam combination for high-power short-pulse laser. The adaptive gain can guarantee the stability and improve the convergence speed of the algorithm. The effective control bandwidth decreases with increasing intensity or frequency of phase noise, and increases with increasing iteration rate and decreasing of beam number. Limited by the performance of device,SPGD algorithm cannot be applied to the coherent beam combination for more than four beams laser array with the bandwidth of 30 fs.