Quantitative phase imaging and measurement of surface topography and fluid dynamics for objects, especially for moving objects, is critical in various fields. Although effective, existing synchronous phase-shifting methods may introduce additional phase changes in the light field due to differences in optical paths or need specific optics to implement synchronous phase-shifting, such as the beamsplitter with additional anti-reflective coating and a micro-polarizer array. Therefore, we propose a synchronous phase-shifting method based on the Mach–Zehnder interferometer to tackle these issues in existing methods. The proposed method uses common optics to simultaneously acquire four phase-shifted digital holograms with equal optical paths for object and reference waves. Therefore, it can be used to reconstruct the phase distribution of static and dynamic objects with high precision and high resolution. In the experiment, the theoretical resolution of the proposed system was 1.064 µm while the actual resolution could achieve 1.381 µm, which was confirmed by measuring a phase-only resolution chart. Besides, the dynamic phase imaging of a moving standard object was completed to verify the proposed system’s effectiveness. The experimental results show that our proposed method is suitable and promising in dynamic phase imaging and measurement of moving objects using phase-shifting digital holography.