Pose and expression normalization is a crucial step to recover the canonical view of faces under arbitrary conditions, so as to improve the face recognition performance. An ideal normalization method is desired to be automatic, database independent and should preserve the face appearance with little artifact and information loss, which we call high-fidelity. However, most normalization methods fail to satisfy one or more of the goals.In this paper, we propose a High-fidelity Pose and Expression Normalization (HPEN) method with 3D Morphable Model (3DMM) which can automatically generate a natural face image in frontal pose and neutral expression.Specifically, we firstly make a landmark marching assumption to describe the non-correspondence between 2D and 3D landmarks caused by pose variations and propose a pose adaptive 3DMM fitting algorithm. Secondly, we mesh the whole image into a 3D object and eliminate the pose and expression variations using an identity preserving 3D transformation. Finally, we propose an inpainting method based on Possion Editing to fill the invisible region caused by self occlusion. Extensive experiments on Multi-PIE and LFW demonstrate that the proposed method significantly improves face recognition performance and outperforms state-of-the-art methods in both constrained and unconstrained environments.