As a classic statistical model of 3D facial shape and texture, 3D Morphable Model (3DMM) is widely used in facial analysis, including model fitting, image synthesis, etc. Conventional 3DMM is learned from a collection of wellcontrolled 2D face images with associated 3D face scans, and represented by two sets of PCA basis functions. Due to the type and amount of training data, as well as, the linear bases, the representation power of 3DMM can be limited. To address these problems, this paper proposes an innovative framework to learn a nonlinear 3DMM model from a large set of unconstrained face images, without collecting 3D face scans. Specifically, given a face image as input, a network encoder estimates the projection, shape and texture parameters. Two network decoders serve as the nonlinear 3DMM to map from the shape and texture parameters to the 3D shape and texture, respectively. With the projection parameter, 3D shape, and texture, a novel analyticallydifferentiable rendering layer is designed to reconstruct the original input face. The entire architecture is end-to-end trainable with only weak supervision. We demonstrate the superior representation power of our nonlinear 3DMM over its linear counterpart, and its contribution to face alignment and 3D face reconstruction.