Although multimodal large language models (MLLMs) have achieved promising results on a wide range of vision-language tasks, their ability to perceive and understand human faces is rarely explored. In this work, we comprehensively evaluate existing MLLMs on face perception tasks. The quantitative results reveal that existing MLLMs struggle to handle these tasks. The primary reason is the lack of image-text datasets that contain fine-grained descriptions of human faces. To tackle this problem, we design a practical pipeline for constructing datasets, upon which we further build a novel multimodal large face perception model, namely Face-MLLM. Specifically, we re-annotate LAION-Face dataset with more detailed face captions and facial attribute labels. Besides, we re-formulate traditional face datasets using the question-answer style, which is fit for MLLMs. Together with these enriched datasets, we develop a novel three-stage MLLM training method. In the first two stages, our model learns visual-text alignment and basic visual question answering capability, respectively. In the third stage, our model learns to handle multiple specialized face perception tasks. Experimental results show that our model surpasses previous MLLMs on five famous face perception tasks. Besides, on our newly introduced zero-shot facial attribute analysis task, our Face-MLLM also presents superior performance.