The paper aims to study the spectral reflectance reconstruction algorithm and improve the accuracy of spectral reflectance reconstruction. Firstly, the channel information and spectral reflectance of Munsell color card and SG140 color card were obtained by multi-spectral camera and spectrophotometer respectively. After normalization, the channel information and spectral reflectance value of Munsell color card were used as the input and output of training samples. Then, the APSO algorithm was used to optimize the optimal regularization parameters and nuclear parameters of LSSVM, and the spectral reflectance reconstruction model based on APSO-LSSVM was constructed. During the process of the model parameters optimization, in order to maintain the activity of the particle, adaptive inertia weights were introduced into the particle swarm algorithm, and mutation operations were added according to the mutation ideas in genetic algorithms, and some mutation factors were introduced into ordinary particles. In each iteration of the update, the particles were initialized with a certain probability, so that the particle swarm algorithm could jump out of the local optimal solution and optimize in a larger space. Finally,, the average color difference of the method was 0.4677 based on the APSO-LSSVM model to perform spectral reflectance reconstruction experiments on the SG140 color card, and the average root mean square error was 0.0006. Compared with the LSSVM model and the BP neural network model, the reconstruction accuracy was greatly improved. From the perspective of color rendering effect, the color rendering result of the method in this paper was closer to the real color, and the difference between the two was hardly noticeable to the human eye. The spectral reflectance reconstruction model based on APSO-LSSVM could effectively improve the spectral reflectance reconstruction accuracy, and realize the reconstruction of multi-channel information captured by multispectral camera to obtain accurate multispectral images.