Sinusoidal phase-shifting interferometry (SinPSI) suffered from modulation error. To cope with this problem, an arbitrary sinusoidal modulation SinPSI (ASM-SinPSI) method was proposed, which extracted wavefront phase from Fourier spectrum of the interferometric signal. In ASM-SinPSI, firstly the modulation amplitude was determined from the strength ratio of the first and third spectrum peaks. To avoid being divided by zero in calculating the ratio, a spatially random sampling strategy was adopted. Then the absolute values and signs of sine and cosine of wavefront phase were determined from the first three spectrum peaks, and the phase was calculated with arctangent. Simulations demonstrated that the wavefront phase retrieval error is 0.016 rad without prior knowledge of the modulation. In experiments with modulation amplitudes of 1.6, 2, 2.5 and 3 rad, wavefront phases were accurately measured with ASM-SinPSI, and the maximum deviation from the exact phase was 0.058 7 rad. ASM-SinPSI, having the benefit of extracting wavefront phase with arbitrary unknown modulation amplitude between 1.5-3.5 rad, relaxed the demanding requirement on the phase shifter of interferometers.