The geographically dispersed resources and ever-changing context incur unique heterogeneity, potential fragility, and vulnerability of an edge-cloud system. Thus, the reliability guarantee of services in the edge-cloud is critical. This paper firstly proposes a QoS-aware scheduling model with fault-tolerance in the edge-cloud, which extends the traditional primary-backup (PB) fault-tolerant model to improve the service reliability in the edge-cloud with the time constraints of tasks being satisfied. Then, a QoS-aware fault-tolerant scheduling algorithm including primary copy placement, backup copy placement and an adjustment mechanism is proposed to improve the QoS levels of tasks in the edge-cloud. The primary copy placement is to guarantee the earlier execution of the primary copy of a task to better satisfy the time requirements of tasks. The backup copy placement is to ensure the later execution of the backup copy of a task, reducing the overlapping of the two copies of a task, realizing the improvement of the resource utilization in the edge-cloud under the condition of redundancy and deadline requirements of tasks. The adjustment mechanism is triggered to rearrange the task copies of a computing node of the edge-cloud after the deallocation of a backup copy on the node, to better assist the goal-achievement of the primary and backup copy scheduling. Finally, through extensive simulation experiments with the real world taxi traces, the performance difference between the proposed method and the other four methods are evaluated. Results show that the proposed method generally outperforms the other methods in terms of guarantee ratio, average QoS level, and reliability cost. INDEX TERMS Edge-cloud, QoS, fault-tolerance, time constraint, primary-backup.