As a preferred wavefront sensing (WFS) method, the modified G-S (MGS) algorithm, which is classified as the iterative-transform algorithm of phase-diverse phase retrieval (PDPR), retrieves the phase distribution at pupil from some known point spread function (PSFs) at defocus planes. By using multiple diversities and proper phase unwrapping methods, this algorithm can produce unique phase estimation within a large dynamic range. But for non-connected pupil, the path-independent phase unwrapping inside MGS is invalid owing to fake value of the points located in obstructed areas of pupil. Some detailed modifications about MGS are given. Then, a modified path-independent phase unwrapping algorithm is proposed based on the principle of least difference phase transition (LDPT), which can automatically optimize unwrapping steps and paths according to the pupil structure. Experiments have been implemented for MGS, and the adaptability of the proposed phase unwrapping algorithm has been validated. Compared with the measurement of interferometer, the WFS accuracy of MGS algorithm is calibrated.