The interference intensity is not strictly cosine distribution if multi-beam interference exists in Fizeau interferometer. Based on the formula of interference intensity in Fizeau interferometer, the conditions to make the interference intensity in Fizeau interferometer be approximated as the ideal formula of multi-beam interference are brought. The calculated phase errors of 4-frame phase-shifting algorithms when using multi-beam interferograms are derived, and phase extraction algorithms of multi-beam interference based on π/4 phase-shifting averaging are proposed: two sequences of phase-shifting interferograms with π/4 interval are collected, and the two calculated phases obtained from the two sequences are averaged to suppress the error induced by multibeam interference. The calculated phase errors for test surfaces with different reflection coefficients are numerically simulated in the condition of random phase-shifting errors. A mirror with high reflection coefficient is tested by Fizeau interferometer, and 22 frames of interferograms are captured to calculate the wavefront map. The results indicate that ripple errors at 4 times the modulation frequency of fringes exist in the calculated phase when using routine phase-shifting algorithms, while the proposed π/4 phase-shifting averaging method based on the overlapping averaging 4-frame algorithm can efficiently suppress the phase error caused by multi-beam interference.