A wavefront reconstruction algorithm based on sub-aperture stitching is proposed to reconstruct a phase from its phase differences to improve calculation efficiency. The proposed algorithm is similar to the sub-aperture stitching interferometry. It divides large phase grids into several small sub-apertures, reconstructs the phase of each sub-aperture from the phase differences through the standard wavefront reconstruction algorithm, and then stitches the results of the sub-apertures together. The proposed algorithm can efficiently reconstruct the phase with much less computer memory and calculation time. Simulations and experiments are conducted to demonstrate the effectiveness of the proposed algorithm.