The process of acquiring hyperspectral data cube of a Large Aperture Static Imaging Spectrometer (LASIS) includes several vital and essential steps, such as interferometer modulation, rectangular convolution sampling by pixels of detector and spectra retrieving. In this process, how to precisely evaluate the Signal-Noise Ratio (SNR) of spectra and how to wholly establish a related evaluation model were both generally very complicated. After a full consideration of the transmission process, utilizing the theory of rectangular convolution sampling and the spectral retrieving method regarding the computation of real part of the discrete Fourier transform of interferogram, formulas of both spectral signal and spectral noise were deduced theoretically, and then a evaluation model regarding the spectral SNR of LASIS was established. By using this model and other design factors of LASIS involving the wavenumber related optical transmittance, the interferometer beam splitter efficiency, the detector quantum efficiency and the main circuit noise, a simulation of spectral SNR was implemented. The simulation result was compared with the measurement result of the SNR of a LASIS instrument. The SNR lines and trends of the two match each other basically in single spectral band. The average deviation between them is proved to be 358%. This comparison result demonstrates the feasibility and effectiveness of the evaluation model. This SNR evaluation model consisting of the main technical aspects of typical LASIS instrument from the input spectral radiation to the output spectrum data is possible to be applied widely in practical design and implement of LASIS, as well as may provide valuable reference on SNR calculation and evaluation for other imaging spectrometers.