In the interference phase measurement of slow-changing process, by use of the phase-shifting technology in the initial state, the background and amplitude of interference fringes can be obtained, and a novel phase unwrapping method based on cosine function is proposed. The holograms of the changing process are recorded, and then the phase cosine functions can be obtained by removing the background and amplitude from the holograms. The arccosine functions of phase cosine functions, which are called phase cosine wrapping function in this paper, can be unwrapped by utilizing the additional normal orientation information. The experimental analyses show that the residual noise and the phase-shifting errors have great influence on the accuracy of unwrapped phase. The tangent wrapping phase can’t be filtered by traditional method due to the π phase jumps, and the existing phase unwrapping algorithms are very complex. The phase-shifting errors can only influence the positions of phase jump points in the tangent wrapping phase. It is difficulty to optimize the tangent wrapping phase further. Compared with tangent wrapping phase, the phase cosine wrapping function is consecutive and can be filtered, and the unwrapping process is easier than that of tangent wrapping phase. The influence of phase-shifting errors on phase cosine function is not only positions but values of the wave crest and wave trough. The more precise the phase-shifting is, the closer the values of cosine function to ±1 at wave crest and wave trough are. The Experiment results show that cosine unwrapping method has the equivalent precision with tangent unwrapping method.