When we design a binary phase holographic optical low-pass filter (HOLF), the phase difference is generally set to be $pi$ to optimize the diffraction efficiency. However, the phase difference of real HOLF mostly deviate from $pi$ by the error in the fabrication process. The deviation causes the (0,0)-th order diffracted beam to increase, which results In raising the diffraction efficiency. To study the effects of the phase error on the performance of HOLF, we calculated the MTF of HOLF for various phase differences. The results show that the phase error of 10 $\%$ makes little change in the filtering characteristics of HOLF. Considering the filtering by lens and CCD, the effects of the phase error becomes much smaller. To confirm it experimentally, we fabricated HOLFs for various phase differences. After installing it in a digital camera, we take picture of test targets and observe the Moire fringes and the resolution. The results agree with our prediction.