Due to high performance and low power consumption, heterogeneous processors are widely used in many real-time systems. In these systems, if tasks are not completed before deadline, it will cause disastrous consequences, and thus it is important to provide fault-tolerance. This paper proposes a novel, adaptive and transient fault-tolerant scheduling algorithm to solve the fault-tolerant problem in heterogeneous real-time systems, aiming to improve system reliability within a given deadline. Since task replication is efficient in improving system reliability, the proposed algorithm supports multiple replicas for each primary task and allows the primary tasks and their replicas to be scheduled on the same processor to increase reliability and lower latency. Also, the algorithm can dynamically adjust the number of replicas for each task to accommodate the deadline and ensure higher reliability. Simulated results show that the proposed algorithm can achieve higher reliability in comparison with existing and related fault-tolerant algorithms. To be specific, the proposed algorithm can obtain the reliability of 89.37% whereas the two existing algorithms DB-FTSA and FTSA obtain the reliability of 47.05% and 84.75% for the benchmark of sixty tasks, respectively, to be detailed in Fig. 4 in experiment.