Compared with tristimulus, spectrum contains much more information of a color, which can be used in many fields, such as disease diagnosis and material recognition. In order to get an accurate and stable reconstruction of spectral data from a tristimulus input, a method based on locally linear approximation is proposed in this paper, namely SR-LLA. To test the performance of SR-LLA, we conduct experiments on three Munsell databases and present a comprehensive analysis of its accuracy and stability. We also compare the performance of SR-LLA with the other two spectral reconstruction methods based on BP neural network and PCA, respectively. Experimental results indicate that SR-LLA could outperform other competitors in terms of both accuracy and stability for spectral reconstruction.