The edge computing paradigm is featured by the ability to off-load computing tasks from mobile devices to edge clouds and provide high cost-efficient computing resources, storage and network services closer to the edge. A key question for workflow scheduling in the edge computing environment is how to guarantee user-perceived quality of services when the supporting edge services and resources are with unstable, time-variant, and fluctuant performance. In this work, we study the workflow scheduling problem in the multi-user edge computing environment and propose a Deep-Q-Network (DQN) -based multi-workflow scheduling approach which is capable of handling time-varying performance of edge services. To validate our proposed approach, we conduct a simulative case study and compare ours with other existing methods. Results clearly demonstrate that our proposed method beats its peers in terms of convergence speed and workflow completion time.