Mobile edge computing is becoming a promising computing architecture to overcome the resource limitation of mobile devices and bandwidth bottleneck of the core networks in mobile cloud computing. Although offloading applications to the cloud can extend the performance for the mobile devices, it may also lead to greater processing latency. Usually, the mobile users have to pay for the cloudlet resource or cloud resource they used. In this paper, we bring a thorough study on the energy consumption, time consumption, and cost of using the resource of cloudlet and cloud for workflow applications in mobile edge computing. Based on theoretical analysis, a multi-objective optimization model is established. In addition, a corresponding multi-objective computation offloading method based on non-dominated sorting genetic algorithm II is proposed to find the optimal offloading strategy for all the workflow applications. Finally, extensive experimental evaluations are performed to show that our proposed method is effective and energy-and cost-aware for workflow applications in MEC.