In sinusoidal phase modulating (SPM) interferometry, the spectrum leakage is generated due to the frequency variation of modulating signal or sampling signal. The spectrum leakage induces errors in the measurement result by reducing values of harmonic components. The spectrum leakage in a SPM interferometer and its influence on measurement accuracy are analyzed theoretically with the discrete Fourier transform method. The mathematical expression of the measurement error induced by frequency leakage is obtained. In experiments, when the frequency shift is -0.3～0.3 Hz, the induced measurement error is 0.3～7.9 nm. Beyond the range, the measurement error increases obviously. The experimental and theoretical data agree well with each other.