Mobile Edge Computing (MEC) is a promising architecture to reduce the energy consumption of mobile devices and provide satisfactory quality-of-service to time-sensitive services. How to jointly optimize task offloading and resource allocation to minimize the energy consumption subject to the latency requirement remains an open problem, which motivates this paper. When the latency constraint is taken into account, the optimization variables, including offloading ratio, transmission power, and subcarrier and computing resource allocation, are strongly coupled. To address this issue, we first decompose the original problem into three subproblems named as offloading ratio selection, transmission power optimization, and subcarrier and computing resource allocation. Then, we propose an iterative algorithm to deal with them in a sequence. To be specific, we derive the closed-form solution of offloading ratios, employ the equivalent parametric convex programming to obtain the optimal power allocation policy, and deal with subcarrier and computing resource allocation by the primal-dual method. Simulation results demonstrate that the proposed algorithm can save 20%–40% energy compared with the reference schemes, and can converge to local optimal solutions.