When designing a fault-tolerant scheduling algorithm in a real-time heterogeneous system, it is necessary to consider the constraints of real-time and maximize the reliability of the system. Furthermore, parallel application scheduling problems in heterogeneous systems have been shown to be NP-complete. Most of the existing fault-tolerant scheduling algorithms use replication technology to improve the reliability of the system, but the multiple execution of tasks will lead to longer application execution time and reduced system real-time performance. Therefore, a fault-tolerant scheduling algorithm based on active replication technology is proposed. The algorithm continuously replicates the tasks that have the least impact on the real-time performance of the current system in the task set and then schedules all tasks in the task set to the earliest completed processor. While meeting the real-time constraints, the algorithm improves the reliability of the system. Experiments show that the reliability of the proposed algorithm has been improved under strict time constraints compared with that of the DB-FTSA algorithm which also focuses on real-time heterogeneous systems.