In this study, we proposed a new method to recover the spectral reflectance by simulating the nonparametric metameric spectra of extreme points (NMSEP) with a linear interpolation method, called the INMSEP method. The concept of introducing the spectra of extreme points as training samples greatly expands the proportion of the reconstructed gamut, and effectively solves the shortcomings of the previous methods. In addition, we conducted experiments that selected the color chips material and compared the reconstructed results of various types of materials. The effectiveness of this suggested method was evaluated with a comparison of the previous linear interpolation, classical PCA, and weighted PCA methods. There is a color difference under illuminant A and TL84. The RMSE and the GFC values are used as the criteria of the recovered spectrum. The experimental results show that the suggested method has high accuracy in reconstructing the spectral reflectance for materials of artificial colors, such as color chips and silk cloth. The results are good in both colorimetric accuracy and fitness of spectrum. The human eye cannot distinguish the difference between the original and the recovered colors. However, the reconstruction of natural color dataset of our method is not obviously effective compared to the PCA-based method. This needs to be improved in the future.