The proposed supervisory control system (SCS) uses a control map to maximize the powertrain efficiency of a hybrid electric vehicle (HEV) in real-time. The paper presents the methodology and structure of the control, including a novel, comprehensive and unified expression for the overall powertrain efficiency that considers the engine-generator set and the battery in depth as well as the power electronics. A control map is then produced with instructions for the optimal power share between the engine branch and battery branch of the vehicle such that the powertrain efficiency is maximized. This map is computed off-line and can thereafter be operated in real-time at very low computational cost. A charge sustaining factor is also developed and introduced to ensure the SCS operates the vehicle within desired SOC bounds. This SCS is then tested and benchmarked against two conventional control strategies in a high-fidelity vehicle model, representing a series HEV. Extensive simulation results are presented for repeated cycles of a diverse range of standard driving cycles, showing significant improvements in fuel economy (up to 20%) and less aggressive use of the battery. (C) 2014 Elsevier Ltd. All rights reserved.