When the vortex beam passes through atmospheric turbulence, the wavefront will be distorted, and the distorted wavefront needs to be corrected. The wavefront distortion correction system of wavefrontless sensors based on the stochastic parallel gradient descent algorithm can realize the correction of wavefront distortion, but the convergence speed and stability of the algorithm are affected by the random disturbance voltage. Combined with the improved gradient descent algorithm in deep learning theory, the iteration method of the random disturbance voltage in the stochastic parallel gradient descent algorithm is adjusted in this paper, and the correction effect of the improved algorithm under different turbulence intensities is analyzed. The simulation results show that the improved algorithm based on RMSprop is preferred under weak turbulence condition. Under moderate turbulence and strong turbulence conditions, it is necessary to consider the stability of the algorithm, the value of the performance evaluation function, and the convergence speed in accordance with actual requirements, and then select the appropriate correction algorithm.