The maximization of the Quality of Service (QoS) for multi-tenants is one of the key issues for cloud-edge service providers. Limited computing resources, different priorities, and deadlines of tenants make it difficult to satisfy the demands of all the multi-tenants. This paper considers the problem of scheduling limited cloud-edge resources to multi-tenant workflow applications with priority and deadline constraints. A level-based iterative greedy algorithm for the problem is proposed. The algorithm defines a priority-based multi-tenant instance success entropy to measure the total quality of service. The destruction & reconstruction and local search of the algorithm is performed based on the level of tasks. The proposed algorithm is compared to modified classical algorithms for similar problems. Experimental results demonstrate the effectiveness of the proposal for the considered problem.