Automatic lip-reading (ALR) aims to recognize words using visual information from the speaker's lip movements. In this work, we introduce a novel type of sensing device, event cameras, for the task of ALR. Event cameras have both technical and application advantages over conventional cameras for the ALR task because they have higher temporal resolution, less redundant visual information, and lower power consumption. To recognize words from the event data, we propose a novel Multi-grained Spatio-Temporal Features Perceived Network (MSTP) to perceive fine-grained spatio-temporal features from microsecond time-resolved event data. Specifically, a multi-branch network architecture is designed, in which different grained spatio-temporal features are learned by operating at different frame rates. The branch operating on the low frame rate can perceive spatial complete but temporal coarse features. While the branch operating on the high frame rate can perceive spatial coarse but temporal refinement features. And a message flow module is devised to integrate the features from different branches, leading to perceiving more discriminative spatio-temporal features. In addition, we present the first event-based lip-reading dataset (DVS-Lip) captured by the event camera. Experimental results demonstrated the superiority of the proposed model compared to the state-of-the-art event-based action recognition models and video-based lip-reading models.