Utilizing a spectral dictionary learned from a couple of similar-scene multi- and hyperspectral image, it is possible to reconstruct a desired hyperspectral image only with one single multispectral image. However, the differences between the similar scene and the desired hyperspectral image make it difficult to directly apply the spectral dictionary from the training domain to the task domain. To this end, a compensation matrix based dictionary transfer method for the similar-scene multispectral image spectral super-resolution is proposed in this paper, trying to reconstruct a more accurate high spatial resolution hyperspectral image. Specifically, a spectral dictionary transfer scheme is established by using a compensation matrix with similarity constraint, to transfer the spectral dictionary learned in the training domain to the spectral super-resolution domain. Subsequently, the sparse coefficient matrix is optimized under sparse and low-rank constraints. Experimental results on two AVIRIS datasets from different scenes indicate that, the proposed method outperforms other related SOTA methods.