Hyperspectral sparse unmixing methods have attracted considerable attention， and most current sparse unmixing methods are implemented in the spatial domain； however， the hyperspectral data used by these methods complicate feature extraction owing to scattered information， redundancy， and noisy spatial signals. To improve the robustness and sparsity of the unmixing results of hyperspectral images， a spectral-weighted sparse unmixing method of hyperspectral images based on the framelet transform （SFSU） is proposed. First， we introduce the theoretical knowledge of hyperspectral sparse unmixing and the framelet transform. Following this， we develop a hyperspectral image unmixing model based on the framelet transform using this theory. In this model， a spectral-weighted sparse regularization term is added to construct the SFSU. Finally， to solve the SFSU model， an alternating direction method of multipliers is presented. According to the experimental results， the signal-to-reconstruction error ratio is found to increase by 12.4%-1 045%， and the probability of success （P_s） remains within 16% error. The proposed model demonstrates better anti-noise and sparse performance compared with other related sparse unmixing methods and yields better unmixing results.