Recent years have witnessed significant progress in image-based 3D face reconstruction using deep convolutional neural networks. However, current reconstruction methods often perform improperly in self-occluded regions and can lead to inaccurate correspondences between a 2D input image and a 3D face template, hindering use in real applications. To address these problems, we propose a deep shape reconstruction and texture completion network, SRTC-Net, which jointly reconstructs 3D facial geometry and completes texture with correspondences from a single input face image. In SRTC-Net, we leverage the geometric cues from completed 3D texture to reconstruct detailed structures of 3D shapes. The SRTC-Net pipeline has three stages. The first introduces a correspondence network to identify pixel-wise correspondence between the input 2D image and a 3D template model, and transfers the input 2D image to a $U$- $V$ texture map. Then we complete the invisible and occluded areas in the $U$- $V$ texture map using an inpainting network. To get the 3D facial geometries, we predict coarse shape ( $U$- $V$ position maps) from the segmented face from the correspondence network using a shape network, and then refine the 3D coarse shape by regressing the $U$- $V$ displacement map from the completed $U$- $V$ texture map in a pixel-to-pixel way. We examine our methods on 3D reconstruction tasks as well as face frontalization and pose invariant face recognition tasks, using both in-the-lab datasets (MICC, MultiPIE) and in-the-wild datasets (CFP). The qualitative and quantitative results demonstrate the effectiveness of our methods on inferring 3D facial geometry and complete texture; they outperform or are comparable to the state-of-the-art.