The likelihood of traffic crashes is significantly affected by the short-term turbulence of traffic flow, a common phenomenon on freeways due to high traffic volume and speed. Real-time traffic safety models have the potential to capture this variation in traffic flow to predict crashes reliably, but data collection methods used in previous studies cannot effectively reflect the necessary spatio-temporal traffic dynamics. Floating car data (FCD), utilizing the kinematics information collected by multiple single vehicles, provides a way to acquire this information on traffic flow before crashes occur. This study aims to develop a real-time crash prediction model based on FCD from the Jiading-Jinshan and Outer Ring Freeways in Shanghai, China. A map matching technique is employed for freeway FCD without heading direction. Both dynamic and static features are constructed, and the variations of dynamic features before the crash are analyzed. The non-parameter tests (Mann–Whitney U and Fligner–Killeen tests) are applied to identify the heterogeneity between crash and non-crash cases. The bidirectional long short-term memory network (LSTM) with a multi-head attention mechanism combined with dynamic and static features is built and showed the best performance. Different histogram-based threshold selection methods are compared. The trained model is applied to all the data for validation, and the matched case-control technique can well predict crashes in this study. The main findings are: (1) the multi-head attention and bidirectional mechanisms can significantly improve model performance, while the static features combination is not as effective; (2) volume is the most important dynamic feature, then is the speed standard deviation followed by the average speed. This model can be applied in providing alerts to drivers and evaluating real-time intervention measures.