Face detection is essential to facial analysis tasks such as facial reenactment and face recognition. Both cascade face detectors and anchor-based face detectors have translated shining demos into practice and received intensive attention from the community. However, cascade face detectors often suffer from a low detection accuracy, while anchor-based face detectors rely heavily on very large networks pre-trained on large scale image classification datasets such as ImageNet [1], which is not computationally efficient for both training and deployment. In this paper, we devise an efficient anchor-based cascade framework called anchor cascade. To improve the detection accuracy by exploring contextual information, we further propose a context pyramid maxout mechanism for anchor cascade. As a result, anchor cascade can train very efficient face detection models with a high detection accuracy. Specifically, comparing with a popular CNN-based cascade face detector MTCNN [2], our anchor cascade face detector greatly improves the detection accuracy, e.g., from 0.9435 to 0.9704 at 1k false positives on FDDB, while it still runs in comparable speed. Experimental results on two widely used face detection benchmarks, FDDB and WIDER FACE, demonstrate the effectiveness of the proposed framework.