Most recent 6D object pose methods use 2D optical flow to refine their results. However, the general optical flow methods typically do not consider the target's 3D shape information during matching, making them less effective in 6D object pose estimation. In this work, we propose a shape-constraint recurrent matching framework for 6D object pose estimation. We first compute a pose-induced flow based on the displacement of 2D reprojection between the initial pose and the currently estimated pose, which embeds the target's 3D shape implicitly. Then we use this pose-induced flow to construct the correlation map for the following matching iterations, which reduces the matching space significantly and is much easier to learn. Furthermore, we use networks to learn the object pose based on the current estimated flow, which facilitates the computation of the pose-induced flow for the next iteration and yields an end-to-end system for object pose. Finally, we optimize the optical flow and object pose simultaneously in a recurrent manner. We evaluate our method on three challenging 6D object pose datasets and show that it outperforms the state of the art significantly in both accuracy and efficiency.