A high-precision phase recovery technique suitable for Shack-Hartmann wavefront sensors is proposed to tackle the issue of slow convergence in phase recovery. This technique leverages the wavefront reconstruction algorithm of the Shack-Hartmann wavefront sensor. First, the distorted wavefront is reconstructed, and the reconstructed wavefront is then used as the starting point for the improved adaptive stochastic parallel gradient descent (ASPGD) algorithm. This iterative optimization process achieves high-precision phase recovery. By combining the modal method with the ASPGD optimization algorithm, this technique significantly enhances the accuracy of phase recovery and accelerates its convergence speed. The numerical simulation results demonstrate that this technology improves the phase recovery accuracy by three times, achieving a precision of 2‰λ. Compared with the original stochastic parallel gradient descent algorithm, the proposed ASPGD algorithm exhibits lower sensitivity to random perturbation coefficients, a larger dynamic range, and greater practicality. In addition, when addressing noise-induced modal coupling issues, the ASPGD algorithm exhibits superior noise resistance and higher phase recovery accuracy.