Shape decomposition is a fundamental problem for part-based shape representation. We propose the minimum near-convex decomposition (MNCD) to decompose arbitrary shapes into minimum number of "near-convex" parts. The near-convex shape decomposition is formulated as a discrete optimization problem by minimizing the number of nonintersecting cuts. Two perception rules are imposed as constraints into our objective function to improve the visual naturalness of the decomposition. With the degree of near-convexity a user-specified parameter, our decomposition is robust to local distortions and shape deformation. The optimization can be efficiently solved via binary integer linear programming. Both theoretical analysis and experiment results show that our approach outperforms the state-of-the-art results without introducing redundant parts and thus leads to robust shape representation.