The image plane digital holography is commonly used in digital holographic measurement and imaging. The methods of the discrete Fourier transform and the frequency filtering are usually used for reconstructing the object wave in image plane digital holography, and the influence of these algorithms on phase reconstruction is discussed in this paper. Firstly, the influence of the frequency spectrum leakage on phase reconstruction error is analyzed. The results show that the error of the phase reconstruction is very small when the sampling periodicity is an integer, so high accuracy of phase reconstruction can be achieved in this case. But when the sampling periodicity is not an integer, the phase reconstruction error is increased obviously. In order to reduce the phase error caused by the frequency spectrum leakage, the Hanning window is used in the pretreatment of the digital hologram. The result shows that the Hanning window can improve the accuracy of the reconstruction phase effectively.