A novel phase-unwrapping method is proposed to improve the speed of three-dimensional measurement by reducing the number of fringe images required for projection and acquisition in phase-shifting profilometry. First, an additional cosine-coded image with a fixed position frequency jump is projected under a three-step phase-shifting mode. The cosine truth value is calculated from four captured images. Second, the cosine relationship between the absolute phase and cosine truth value at different frequencies within different periods is utilized. Phase discontinuity points are obtained, whereby phase unwrapping is performed through an iterative interpolation method. Finally, the order jump errors that occur near the discontinuity points are corrected using a three-phase method. In line with the experimental results, the proposed method required only four images for temporal phase unwrapping in multi-frequency mode and was unaffected by phase interruptions. When the number of phase-shifting image period was 15, the phase calculation results were consistent with the multi-frequency progressive method.