Interferometric imaging spectrometer has the advantage of high flux, high spectral resolution and high target resolution when it is used for narrow-band hyperspectral imaging detection. When the fringe pattern is sampled according to the Nyquist law, it produces large data redundancy which increases the data of Fourier transform and affects the spectrum recovery efficiency. To improve the recovery efficiency of interferometric imaging spectrometer, a narrow-band compressive sampling method based on the transmittance function of optical band-pass filter is described after analyzing the Fourier transform characteristics of narrow-band spectrum. By introducing different parameters of the filter and aliasing parameter, we can get compressive sampling frequency of narrow-band spectrum with different recovery accuracy. Together with the optical multi-band-pass narrow-band filter, we can obtain multiple-band spectrums information of the target through direct compressive sampling in order to avoid the by-band detection and to improve the detection efficiency. The proposed method is verified by simulation and experiment. As a result, the recovery narrow-band spectrum is consistent with the target spectrum.