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Mobile Edge Computing (MEC), which is considered a promising and emerging paradigm to provide caching capabilities in proximity to mobile devices in 5G networks, enables fast, popular content delivery of delay-sensitive applications at the backhaul capacity of limited mobile networks. Most existing studies focus on cache allocation, mechanism design and coding design for caching. However, grid power supply with fixed power uninterruptedly in support of a MEC server (MECS) is costly and even infeasible, especially when the load changes dynamically over time. In this paper, we investigate the energy consumption of the MECS problem in cellular networks. Given the average download latency constraints, we take the MECS’s energy consumption, backhaul capacities and content popularity distributions into account and formulate a joint optimization framework to minimize the energy consumption of the system. As a complicated joint optimization problem, we apply a genetic algorithm to solve it. Simulation results show that the proposed solution can effectively determine the near-optimal caching placement to obtain better performance in terms of energy efficiency gains compared with conventional caching placement strategies. In particular, it is shown that the proposed scheme can significantly reduce the joint cost when backhaul capacity is low.