This study proposes methods for space-time diffusion measures and a simulation on crime analyses. A spatial pattern of crimes is a constantly changing and ongoing process. However, prior research on spatial crime analysis has focused primarily on identifying fixed spatial patterns, and has neglected temporal aspects. As a result, the literature has difficulty in explaining the formation and development of such spatial crime patterns. This study investigates both spatial and temporal aspects of crime occurrences, particularly on the space-time diffusion process by using the temporal extensions of local spatial autocorrelation measures. In addition, space-time diffusion simulation is applied based on Hagerstrand’s diffusion modeling. Consequently, diffusion modeling and the simulation (1) enables further understanding of the mechanism of how crime patterns are formed, (2) provides an in depth resource for policy makers and police to reduce crimes by considering a temporal dimension of crime, (3) and is readily applicable to other fields such as the epidemiology of disease.