For gamut mapping of spectral color management, this study propose a nonlinear multispectral dimension reduction method that tackles serial problems in the calculation of high-dimensional spectral data in the process of establishing a look-up table. The method performs a partial least squares analysis on metameric black, extracts the potential components, obtains the KMN vector, and combines the result with Lab vector, yielding a six-dimensional vector which is used as an intermediate conversion space LabKMN. Within this space, the interconversion between the high-dimensional spectral data and low-dimensional base vector can be realized. The LabPQR space is divided into two three-dimensional spaces. The first three dimensions are the CIELAB values under specific lighting conditions, and the remaining dimensions (PQR) describe the spectral reconstruction dimensions of metameric black. The spectral and colorimetric accuracies of the two methods are compared. On 1600 Munsell sample dataset, the proposed method achieves a root-mean-square error of 0.0139 (versus 0.0164 in LabPQR), and a colorimetric reconstruction error of 1.8138 (versus 2.8706 in LabPQR). Compared with LabPQR, the proposed method improves the spectral accuracy by 15.24% and reduces the colorimetric reconstruction error by 36.81%. The reconstruction accuracy is greatly improved after dimension reduction by the proposed method, and the original color spectrum space is described with higher precision.