In the design of the interferometric spectrometer, if the spectral range of filters in the instrument is not significantly greater than the output spectral range of the spectrometer, there exists a problem of mismatch between the spectral range of the filter and the spectrometer, resulting in a significant weakening of the edge spectral response and affecting the spectral accuracy of the edge spectrum. This paper makes a theoretical analysis of the weakening of the edge spectral response, and proposes a method to reduce this phenomenon. The core idea of this method is to simulate the interference data of the edge spectrum through the spectrum and phase data, overlapped with the interference information of the spectrometer to obtain the interference data, which is compensated by the edge spectrum. The data of HJ-1A satellite hyperspectral imager are processed and analyzed by this method. As a result, the image quality of the edge bands improved. In the end, the interference simulation data of the spectrometer are generated and they are analyzed and processed by this method. The results prove that the method can make the edge spectral quality significantly improved.