Patch-based sparse representation modeling has shown great potential in image compressive sensing (CS) reconstruction. However, this model usually suffers from some limits, such as dictionary learning with great computational complexity, neglecting the relationship among similar patches. In this paper, a groupbased sparse representation method with non-convex regularization (GSR-NCR) for image CS reconstruction is proposed. In GSR-NCR, the local sparsity and nonlocal self-similarity of images is simultaneously considered in a unified framework. Different from the previous methods based on sparsity-promoting convex regularization, we extend the non-convex weighted p (0< p <1) penalty function on group sparse coefficients of the data matrix, rather than conventional 1 -based regularization. To reduce the computational complexity, instead of learning the dictionary with a high computational complexity from natural images, we learn the principle component analysis (PCA) based dictionary for each group. Moreover, to make the proposed scheme tractable and robust, we have developed an efficient iterative shrinkage/thresholding algorithm to solve the non-convex optimization problem. Experimental results demonstrate that the proposed method outperforms many state-of-the-art techniques for image CS reconstruction. $ Fully documented templates are available in the elsarticle package on CTAN. Compressive sensing (CS) [1, 2, 3], which aims to recover signals from fewer measurements than suggested by the Nyquist sampling theory, is based on the hypothesis that the signals in question have compressible representations. The most attractive aspect of CS-based compression is that the sampling and compression are conducted simultaneously, and almost all computational cost is derived from the decoder stage, and thus, leading to a low computational cost of the encoder stage. Due to the superior property of CS, it has been widely applied to various areas, such as MRI image [4], remoting sensing [5], single-pixel camera [6] and sensor networks [7].In the theory of CS, if a signal is sparse in some transform domain, it is often sampled by the random projection and reconstructed by solving the 0 minimization problem with the prior information which usually makes up the regularization terms. However, due to the fact that 0 minimization is a difficult combinatorial optimization problem, solving this problem is NP-hard. For this reason, it has been proposed to replace the 0 norm by its convex 1 counterpart to make the optimization easy. For instance, Candès et al. [1] proposed that solving 1 minimization problem can recover a K-sparse signal X ∈ N from M = O(Klog(N/K)) random measurements. To solve the above 1 minimization problem, many CS reconstruction algorithms have been proposed, such as linear programming [3], gradient projection sparse reconstruction [8], match pursuit [9] and iterative thresholding [10].As a basic image inverse problem in the filed of image restoration, maybe the hottest topic is image CS reconstruction, which has a...