In digitally holographic reconstruction, the reconstructed image quality is reduced by the effect of the laser speckle, the system noise and the border diffraction of the digital hologram, which restrains the application of digital holography in phase measurement. In this paper, we apply the apodization for the phase measurement in digital holography to suppress the diffraction and noise effects. Simulations and experiments show that apodization can effectively reduce the border diffraction and noise effects to the reconstructed phase information of the objected wave and improve the measurement precision.