Hyperspectral images (HSI) have high spectral and low spatial resolutions. However, multispectral images (MSI) usually have low spectral and high spatial resolutions. In various applications HSI with high spectral and spatial resolutions are required. In this paper, a new method for spatial resolution enhancement of HSI using high resolution MSI based on sparse coding and linear spectral unmixing (SCLSU) is introduced. In the proposed method (SCLSU), high spectral resolution features of HSI and high spatial resolution features of MSI are fused. In this case, the sparse representation of some high resolution MSI and linear spectral unmixing (LSU) model of HSI and MSI is simultaneously used in order to construct high resolution HSI (HRHSI). The fusion process of HSI and MSI is formulated as an ill-posed inverse problem. It is solved by the Split Augmented Lagrangian Shrinkage Algorithm (SALSA) and an orthogonal matching pursuit (OMP) algorithm. Finally, the proposed algorithm is applied to the Hyperion and ALI datasets. Compared with the other state-of-the-art algorithms such as Coupled Nonnegative Matrix Factorization (CNMF) and local spectral unmixing, the SCLSU has significantly increased the spatial resolution and in addition the spectral content of HSI is well maintained.