Crime risk prediction is helpful for urban safety and citizens’ life quality. However, existing crime studies focused on coarse-grained prediction, and usually failed to capture the dynamics of urban crimes. The key challenge is data sparsity, since that 1) not all crimes have been recorded, and 2) crimes usually occur with low frequency. In this paper, we propose an effective framework to predict fine-grained and dynamic crime risks in each road using heterogeneous urban data. First, to address the issue of unreported crimes, we propose a cross-aggregation soft-impute (CASI) method to deal with possible unreported crimes. Then, we use a novel crime risk measurement to capture the crime dynamics from the perspective of influence propagation, taking into consideration of both time-varying and location-varying risk propagation. Based on the dynamically calculated crime risks, we design contextual features (i.e., POI distributions, taxi mobility, demographic features) from various urban data sources, and propose a zero-inflated negative binomial regression (ZINBR) model to predict future crime risks in roads. The experiments using the real-world data from New York City show that our framework can accurately predict road crime risks, and outperform other baseline methods.