Learning-enabled components have been widely deployed in autonomous systems. However, due to the weak interpretability and the prohibitively high complexity of large- scale machine learning models such as neural networks, relia- bility has been a crucial concern for safety-critical autonomous systems. This work proposes an online monitor called Reach- Flow for safety verification of waypoint-following tasks for self-driving cars. ReachFlow is independent of the controller in use, that is, we can verify a traditional controller or an opaque machine learning-based controller. ReachFlow uses an efficient prototype tool based on the FLOW* library for non- linear reachability analysis. We implement ReachFlow in a self-driving racing car governed by a reinforcement learning- based controller. We demonstrate the effectiveness by rigorously verifying a safe waypoint-following control and providing a fallback control for an unsafe situation in which a large path deviation is predicted.