In order to improve visible multispectral image (MSI) compression efficiency and further facilitate their storage and transmission for the applications of generic fields, in which both high colorimetric and spectral accuracy are desired, a nonlinear spectral reflectance model is proposed. Then based on this, LabW2P codec is presented, which has the advantages of moderate complexity, good illuminant stability and support for consistent color reproduction across devices. First, according to spectral characteristics of MSIs, a nonlinear spectral reflectance model is proposed for the decomposition and representation of spectral data to different transformation spaces. In the model, spectra are expressed as linear component and difference spectra. The linear component consists of six transformation basis and spectral projection coefficients. And the difference spectra are non-linear represented components. The model provides the theoretical basis for the construction of the coding algorithm and the improvement of spectral and chrominance reconstruction performance. Then, according to the characteristics of human visual system, illumination conditions, and CIE standard chromaticity space transform function, the three-dimensional (3D) colorimetric information Lab of spectral reflectance is extracted to ensure the colorimetric accuracy of the reconstructed image. Meanwhile, based on the nonlinear spectral model, visual-curve-like trigonometric function basis are used to obtain the first 2D projection coefficients of linear component as the latter 2D coding values that are W1 and W2, which can be utilized to approximate R and G channels, and also improve the colorimetric and spectral reconstruction accuracy. Combined with error compensation mechanism, predicted difference spectral is generated. The Principal Component Analysis (PCA) method is used to extract the first principal component P which compensates for the linear spectral reconstruction error and further improves the spectral accuracy. Finally, the extracted three components are combined to form LabW2P coding. LabW2P decoding scheme is the inverse of the coding. First, according to Lab, W1 and W2, combined with CIELAB to CIEXYZ conversion function, illumination conditions, CIE standard observer color matching function, and trigonometric function basis, the reconstructed projection coefficients on transform space are obtained by using least square regression, and then linear spectral data is rebuilt. Next, based on the value of P, inverse PCA is utilized to gain the reconstructed prediction difference data. Finally, two parts of reconstruction data are combined to get the reconstructed MSI. Experimental results show that the average colorimetric precision of LabW2P algorithm is 0.207 6, which is increased by 81.54%, 55.48% and 32.29% respectively in comparison with that of the classical PCA, LabPQR and LabRGB methods. The maximum average color difference is 0.507 0, and in addition, it is between 0 and 0.5, reaching the color reconstructed level of being visually neglected. Meanwhile, the average spectral precision is 0.012 7, which is slightly weaker than that of PCA, but 13.01% and 6.62% higher than that of LabPQR and LabRGB respectively. The results indicate that LabW2P has obvious advantages of both colorimetric and spectral reconstruction performance. Besides, our coding values can be used directly for object color estimation. And compared with PCA and LabPQR, LabW2P transmits less side information and has higher compression ratio.