In the premise of fulfilling the application requirement, the adjustment of spectral resolution can improve efficiency of data acquisition, data processing and data saving. So, by adjusting the spectral resolution, the performance of spectrometer can be improved, and its application range can be extended. To avoid the problems of the fixed spectral resolution of classical Fourier transform spectrometer, a novel type of spatial modulation Fourier transform spectrometer with adjustable spectral resolution is proposed in this paper. The principle of the novel spectrometer and its interferometer is described. The general expressions of the optical path difference and the lateral shear are induced by a ray tracing procedure. The equivalent model of the novel interferometer is analyzed. Meanwhile, the principle of the adjustment of spectral resolution is analyzed. The result shows that the novel spectrometer has the merits of adjustable spectral resolution, high stability, easy assemblage and adjustment etc. This theoretical study will provide the theoretical basis for the design of the spectrometer with adjustable spectral resolution and expand the application range of Fourier transform spectrometer.