Crime prediction plays an impactful role in enhancing public security and sustainable development of urban. With recent advances in data collection and integration technologies, a large amount of urban data with rich crime-related information and fine-grained spatio-temporal logs have been recorded. Such helpful information can boost our understandings of the temporal evolution and spatial factors of urban crimes and can enhance accurate crime prediction. However, the vast majority of existing crime prediction algorithms either do not distinguish different types of crime or treat each crime type separately, which fails to capture the intrinsic correlations among different types of crime. In this paper, we perform crime prediction exploiting the cross-type and spatio-temporal correlations of urban crimes. In particular, we verify the existence of correlations among different types of crime from temporal and spatial perspectives, and propose a coherent framework to mathematically model these correlations for crime prediction. Extensive experiments on real-world datasets validate the effectiveness of our framework.