It is one of the most important methods to use field-widened prism to increase the throughput or sensitivity for spatial heterodyne spectrometer. This paper borrows idea from the basic principle of traditional Fourier transform spectrometer with field-widened and combines the characteristics of spatial heterodyne spectroscopy, a method based on numerical reduction to design the field-widen prism of spatial heterodyne spectrometer is proposed. The optimum apex angle of field-widened prism and the maximum field are analyzed with certain Littrow angles and scene wave-numbers. The results indicate that numerical induction method can find the optimum solution of prism apex angle by judging the effect of all orders of field angle on the phase difference. Compared with the results obtained by theoretical deduce method, the maximum field angle along dispersive principal cross section increases by 10%~30%, and the numerical induction method is simple and obvious, the influencing factors on the maximum field angle can be analyzed in the process of optimizing field-widened prism angle.