The work aims to establish a spectral gamut mapping model in the modified LMS weighted PCA space with respect to the spectral gamut inconsistency of media in different colors in cross-media spectral color reproduction process. The high-dimensional spectral data was weighted by the modified LMS weighted function after adjustment. Then, the first three principal components of weighted spectra were extracted by using the principal component analysis (PCA) method, so that the LMS-PCA spectral link space was set up. In the LMS-PCA space, the mature segment maxima gamut boundary descriptor (SMGBD) algorithm was adopted to describe the device spectral gamut, and the image color points outside the device spectral gamut were subject to LSLINceLmax gamut compression and then mapped into the device spectral field. LSLINceLmax gamut compression was achieved based on the optimization of traditional LSLIN algorithm. The new model had higher spectral accuracy and chromaticity accuracy than the spectral gamut mapping models using other gamut mapping directions and the spectral gamut mapping model in ordinary visually-featured weighted PCA space. Moreover, it had stable color difference accuracy under changing observation environment. The gamut mapping model in the modified LMS weighted PCA space can basically solve the spectral gamut inconsistency of media in different colors under changing observation environment and it has agreeable practicality.