To obtain the real phase in digital holographic microscopy (DHM), it needs to compensate the additional phase induced by the microscope. Based on the theoretical analysis, both two-step compensation algorithm and Zernike polynomials fitting algorithm are employed to perform the phase reconstruction for biological cell. The obtain results show that both two-step compensation algorithm and Zernike polynomials fitting algorithm are useful for system phase compensation of DHM. In two-step compensation algorithm, since the subtraction operation is performed between the reconstructed phases with the object and without the object, the DHM system phase error can be compensated effectively while it is still time-consuming and needs high experimental stability for recording holograms. In Zernike polynomials fitting algorithm, only one group of digital holograms with the object is required for compensating the additional phase induced by the microscope, therefore it is suitable for the dynamic phase measurement while the constructed phase error increases with both the increase of object height and transverse area. To decrease the reconstruction phase error of Zernike polynomials fitting phase compensation algorithm, it is required to ensure that one of the variations of object optical height or transverse area to be a small value. The result supplies a useful tool for the study and application of biological cell phase compensation by DHM.