Cascade regression is a popular face alignment approach, and it has achieved good performances on the wild databases. However, it depends heavily on local features in estimating reliable landmark locations and therefore suffers from corrupted images, such as images with occlusion, which often exists in real-world face images. In this paper, we present a new adaptive cascade regression model for robust face alignment. In each iteration, the shape-indexed appearance is introduced to estimate the occlusion level of each landmark, and each landmark is then weighted according to its estimated occlusion level. Also, the occlusion levels of the landmarks act as adaptive weights on the shape-indexed features to decrease the noise on the shape-indexed features. At the same time, an exemplar-based shape prior is designed to suppress the influence of local image corruption. Extensive experiments are conducted on the challenging benchmarks, and the experimental results demonstrate that the proposed method achieves better results than the state-of-the-art methods for facial landmark localization and occlusion detection.