3D shape completion is important to enable machines to perceive the complete geometry of objects from partial observations. To address this problem, view-based methods have been presented. These methods represent shapes as multiple depth images, which can be back-projected to yield corresponding 3D point clouds, and they perform shape completion by learning to complete each depth image using neural networks. While view-based methods lead to state-of-the-art results, they currently do not enforce geometric consistency among the completed views during the inference stage. To resolve this issue, we propose a multi-view consistent inference technique for 3D shape completion, which we express as an energy minimization problem including a data term and a regularization term. We formulate the regularization term as a consistency loss that encourages geometric consistency among multiple views, while the data term guarantees that the optimized views do not drift away too much from a learned shape descriptor. Experimental results demonstrate that our method completes shapes more accurately than previous techniques.