Two-dimensional phase unwrapping method is an active and interesting subject, and plays important roles in a great number of measurement applications. Although mask cut algorithm is successful in some applications, the algorithm has its own drawbacks. In order to overcome the drawbacks of the mask cut algorithm that exists in some successful applications, a new two-dimensional quality-guided phase unwrapping algorithm, based on the placement of the branch cuts, is proposed. The new algorithm combines the advantages of the residue-compensation algorithms and those of the quality-guided ones. In the algorithm, an initial quality map of the wrapped phase image is firstly used to guide the placement of the phase unwrapping. Then the minimum quality value is assigned to pixels that belong to the branch cuts to generate a new quality map. Finally, the new quality map is used to guide the phase unwrapping process. The algorithm has been tested by use of several wrapped images. Computer simulation and experimental results make it clear that the proposed algorithm works more effectively than the mask cut algorithm even when complicated discontinuities and high levels of noise exist in the wrapped phase images.