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A novel consistent max-covering method is proposed for human pose estimation. We focus on problems in which a rough foreground estimation is available. Pose estimation is formulated as a jigsaw puzzle problem in which the body part tiles maximally cover the foreground region, match local image features, and satisfy body plan and color constraints. This method explicitly imposes a global shape constraint on the body part assembly. It anchors multiple body parts simultaneously and introduces hyperedges in the part relation graph, which is essential for detecting complex poses. Using multiple cues in pose estimation, our method is resistant to cluttered foregrounds. We propose an efficient linear method to solve the consistent max-covering problem. A two-stage relaxation finds the solution in polynomial time. Our experiments on a variety of images and videos show that the proposed method is more robust than previous locally constrained methods.