As a new computing mode, mobile edge computing (MEC) can use wireless access network to provide user with required services and computing power nearby, thus improve users’ service experience. Mobile devices can offload computation-intensive tasks to MEC for computing. MEC can greatly reduce the energy consumption of mobile devices while also extending their battery life. However, task assignment based on MEC becomes more difficult due to the uncertainty of task arrival and the highly dynamic state of wireless channel. In this chapter, CPU cycle frequency and task allocation are both considered. Our goal is to keep the task queue stable while minimizing energy consumption. Then, we describe the minimization problem as a stochastic optimization problem, and transform it into a deterministic optimization problem by using Lyapunov optimization method. Then, the transformed problem is decoupled into two sub-problems. Then, a Computation Offloading and Frequency Scaling for Energy Efficiency (COFSEE) algorithm for online task offloading and frequency transformation is proposed. Our algorithm can solve optimal subproblems in parallel. We evaluate the performance of COFSEE algorithm through experiments. Experimental results show that the energy consumption of COFSEE is about 15% lower than that of RLE algorithm and 38% lower than that of RME algorithm. Through experiments, we verify the effectiveness of COFSEE algorithm.