Face parsing is an important problem in computer vision that finds numerous applications including recognition and editing. Recently, deep convolutional neural networks (CNNs) have been applied to image parsing and segmentation with the state-of-the-art performance. In this paper, we propose a face parsing algorithm that combines hierarchical representations learned by a CNN, and accurate label propagations achieved by a spatially variant recurrent neural network (RNN). The RNN-based propagation approach enables efficient inference over a global space with the guidance of semantic edges generated by a local convolutional model. Since the convolutional architecture can be shallow and the spatial RNN can have few parameters, the framework is much faster and more light-weighted than the state-of-the-art CNNs for the same task. We apply the proposed model to coarse-grained and fine-grained face parsing. For fine-grained face parsing, we develop a two-stage approach by first identifying the main regions and then segmenting the detail components, which achieves better performance in terms of accuracy and efficiency. With a single GPU, the proposed algorithm parses face images accurately at 300 frames per second, which facilitates real-time applications.