This paper proposes the fine-grained traffic prediction task (e.g. interval between data points is 1 minute), which is essential to traffic-related downstream applications. Under this setting, traffic flow is highly influenced by traffic signals and the correlation between traffic nodes is dynamic. As a result, the traffic data is non-smooth between nodes, and hard to utilize previous methods which focus on smooth traffic data. To address this problem, we propose Fine-grained Deep Traffic Inference, termed as FDTI. Specifically, we construct a fine-grained traffic graph based on traffic signals to model the inter-road relations. Then, a physically-interpretable dynamic mobility convolution module is proposed to capture vehicle moving dynamics controlled by the traffic signals. Furthermore, traffic flow conservation is introduced to accurately infer future volume. Extensive experiments demonstrate that our method achieves state-of-the-art performance and learned traffic dynamics with good properties. To the best of our knowledge, we are the first to conduct the city-level fine-grained traffic prediction.