The phase unwrapping method is the important step of phase retrieval in fringe projection profilometry. Although the mask cut (MC) algorithm has been successfully applied in multiple fields, it also has inherent flaws. In order to overcome the shortcomings of MC algorithm, and synthesize the advantages of MC and quality-guided (QG) algorithm, a quality-guided mask-cutting (QG - MC) algorithm for phase unwrapping is proposed. The basic idea of QG - MC algorithm is to reduce the effects of noise on phase unwrapping at first., Then, the process of phase unwrapping is guided by the phase quality map from the point with the highest quality value to the point around that point. Take the point with the highest quality as the seed point, put its adjacent points into the queue, sort by quality value, and the new highest quality point is used as a seed point. Repeats the process until the queue is empty and the unwrapped phase will be obtained. To verify the feasibility and reliability of QG - MC algorithm, computer simulations and real experiments are carried out. The results show that the algorithm improves the efficiency of phase unwrapping.