This paper presents a single-degree-of-freedom energy optimization strategy to solve the energy management problem existing in power-split hybrid electric vehicles (HEVs). The proposed strategy is based on a quadratic performance index, which is innovatively designed to simultaneously restrict the fluctuation of battery state of charge (SOC) and reduce fuel consumption. An extended quadratic optimal control problem is formulated by approximating the fuel consumption rate as a quadratic polynomial of engine power. The approximated optimal control law is obtained by utilizing the solution properties of the Riccati equation and adjoint equation. It is easy to implement in real-time and the engineering significance is explained in details. In order to validate the effectiveness of the proposed strategy, the forward-facing vehicle simulation model is established based on the ADVISOR software (Version 2002, National Renewable Energy Laboratory, Golden, CO, USA). The simulation results show that there is only a little fuel consumption difference between the proposed strategy and the Pontryagin’s minimum principle (PMP)-based global optimal strategy, and the proposed strategy also exhibits good adaptability under different initial battery SOC, cargo mass and road slope conditions.