Traditional fast Fourier transform (FFT) is only useful in uniform sampled interferogram. For nonuniform sampled interferogram, the spectrum recovered by FFT is often distorted when the aliasing is neglected. To solve the problem, nonuniform fast Fourier transform (NUFFT) method is proposed and some mature theories are formed. The NUFFT is applied to the spectrum recovery of interferogram, and the interferogram at different sampling frequency and different degree of nonuniform optical path difference (OPD) is analyzed and simulated. The results indicate that sampling frequency is the main factor that affect the recovery precision for undersampled interferogram condition, while the nonuniform degree of OPD is more affective for oversampled interferogram condition. In the application, data quantity, sampling frequency and the nonuniform degree of OPD must be considered comprehensively to acquire the final design parameter. To ensure the recovery precision, avoiding the undersampling of gotten interferogram is the basic criteria.