The branch-cut phase unwrapping algorithm is widely used because of its better noise suppression effect. However, the branch-cuts constructed by the branch-cut algorithm may not be the shortest globally, and it is easy to form a closed branch-cuts , resulting in phase unfolding errors. Therefore, an improved branch-cut algorithm based on tabu search is proposed. The nearest neighbor algorithm is used to match the positive and negative residues to obtain the initial solution, and then the tabu search algorithm is used to optimize the initial solution to construct the branch-cuts globally. The algorithm was tested by simulation, and the algorithm reduced the length of the branch-cuts constructed by the branch-cut algorithm by 42% and increased the speed by 28%. And the dynamic three-dimensional shape reconstruction experiment is carried out on the changed facial expressions, and the results show that the improved algorithm has better phase unwrapping accuracy.