Safety-critical systems detect external events, match the targeted event patterns, and give timely responding actions; otherwise catastrophic results will be incurred. With the increasing demand for intelligence in the safety-critical systems, applying rule-based reasoning to these systems has become an inevitable trend. Besides, rule scheduling is the key to assure hard real-time constraints within rule-based reasoning solutions. In this study, a solution to the multi-core rule scheduling problem, named GBRRS (graph-based real-time rule scheduling), was proposed. With the real-time rule reasoning process analyzed, how rules in safety-critical systems can be modeled as tasks using the graph mapping is described first, and the graph-based end-to-end reasoning task model, E2ERTG, is proposed. Then, a multi-core scheduling algorithm, GBRRS, is presented to guarantee each rule's deadline via the control of the reasoning task's deadline. Simulation-based experiments have been conducted to evaluate the performance of GBRRS. The result shows that GBRRS remains a rule success ratio above 80% even with relatively high workload of the rule set and is superior to DM-EDF by average 13%~15% in terms of rule success ratio.