In this paper, a novel constrained Sparse Representation (SR) algorithm based on the joint sparsity and spatial correlation for hyper- spectral image (HSI) classification is proposed. The coefficients in the sparse vector associated with the training samples in the structured dictionary exhibit the group sparsity continuity. However, this joint sparsity of the coefficient vector is not considered in the classical SR classifiers. In addition, spatial correlation has positive effect on HSI classification processing. Thus in the proposed SR model, we consider a joint sparsity regularization term to promote the joint sparsity of the sparse vectors and use space regularization to restrict spatial correlation of the output. The formulated problem is solved via the alternating direction method of multipliers (ADMM). Simulation results show that the proposed algorithm has the improved performance.