In the three-dimensional (3D) reconstruction system for fringe projection, we need to unwrap the original phase to obtain the real 3D image. A path correlation algorithm is a type of useful phase unwrapping algorithm that can accurately rebuild the shape and texture of the target object. However, the path correlation algorithm is limited by the phase noise. Resultantly, we will not find the right path to unwrap the phase when encountering a singular point in the region with low image quality. Therefore, we propose an algorithm that can retrieve exact phase, ignore noise, and compensate fault. Based on a theoretical study, we can provide the actual image of the object and the wrapped phase image, and reconstruct the actual phase information based on the proposed algorithm. To verify the practicability and superiority of this algorithm, the phase rewrapping algorithm is adopted as the performance metric of the algorithm.