Mobile edge computing as a novel computing paradigm brings remote cloud resource to the edge servers nearby mobile users. Within one-hop communication range of mobile users, a number of edge servers equipped with enormous computation and storage resources are deployed. Mobile users can offload their partial or all computation tasks of a workflow application to the edge servers, thereby significantly reducing the completion time of the workflow application. However, due to the open nature of mobile edge computing environment, these tasks, offloaded to the edge servers, are susceptible to be intentionally overheard or tampered by malicious attackers. In addition, the edge computing environment is dynamical and time-variant, which results in the fact that the existing quasistatic workflow application scheduling scheme cannot be applied to the workflow scheduling problem in dynamical mobile edge computing with malicious attacks. To address these two problems, this paper formulates the workflow scheduling problem with risk probability constraint in the dynamic edge computing environment with malicious attacks to be a Markov Decision Process (MDP). To solve this problem, this paper designs a reinforcement learning-based security-aware workflow scheduling (SAWS) scheme. To demonstrate the effectiveness of our proposed SAWS scheme, this paper compares SAWS with MSAWS, AWM, Greedy, and HEFT baseline algorithms in terms of different performance parameters including risk probability, security service, and risk coefficient. The extensive experiments results show that, compared with the four baseline algorithms in workflows of different scales, the SAWS strategy can achieve better execution efficiency while satisfying the risk probability constraints.