Heartbeat is a significant vital sign. The past decade has witnessed wireless heartbeat monitoring becoming more and more feasible. As a contactless approach, it can relieve users from wearing sensors. The unique advantages of milimeter-wave frequency-modulated continous-wave (FMCW) radar over other wireless devices draw our attention. However, there are plenty of limitations in related work based on it. Tiny vibration caused by heartbeat could be easily interrupted by body movements (BMs) and so on. Range bin selection methods in existing work are not robust enough. The inter-beat interval (IBI) estimation need to be further improved. We propose RF-Heartbeat, a robust heartbeat monitoring system based on milimeter-wave FMCW radar. RF-Heartbeat has novel signal process modules, including BMs detection method, and optimal range bin selection method, for obtaining a relatively high-quality heartbeat signal. Then, a global optimization model based on a template matching algorithm is implemented for improving IBI estimation accuracy. In the heartbeat monitoring experiment for a total of 72 hours and 56 minutes involving 10 participants, under a time coverage of 91.2%, the median error of IBI was 12 ms. RF-Heartbeat achieves a higher performance than state-of-the-art heartbeat monitoring systems. It has strong robustness to different individuals in different postures and positions. Our work provides effective solutions to some obstacles in practical applications of contactless heartbeat monitoring. It enables accurate and long-term heartbeat monitoring, which has wide applications in clinical space and daily life.