The fuel economy of a hybrid electric vehicle (HEV) is determined by its energy management strategy (EMS), while the conventional EMS usually suffers from enormous computation loads when solving a nonlinear optimization problem. To resolve this issue, this paper presents a computationally efficient EMS with close-to-optimal performance using very limited computation resources. Relying on the optimal solutions by offline dynamic programming (DP), a constrained model predictive control (MPC) can quickly determine the engine on/off status and then the torque split problem is solved by a value-based Pontryagin’s minimum principle (PMP). Two measures are taken to further reduce the online computation cost: by surface fitting, the tabular value function is replaced by piecewise linear polynomials and thus the memory occupation is greatly reduced; and by model approximation, the nonlinear torque split problem becomes a quadratic programming one that can be more rapidly solved. The testing results from processor-in-the-loop (PIL) simulation indicate that the proposed EMS can generate a fuel efficiency close to the one by DP, but saves 70% onboard memory space and 30% CPU utilization compared with the benchmark EMS without taking the two measures.