This paper presents a model predictive power management strategy for a novel anti-idling system, regenerative auxiliary power system (RAPS), designed for service vehicles. RAPS is able to utilize recovered braking energy for electrified auxiliary systems; this feature distinguishes it from its counterparts - auxiliary power unit (APU) and auxiliary battery powered unit (ABP). To efficiently operate the RAPS, a power management strategy is required to coordinate power flow between different energy sources. Thus, a model predictive controller (MPC) is developed to improve the overall efficiency of the RAPS. As an optimization-based approach, the MPC-based power management strategy usually requires the drive cycle or the drivers’ command to be known a priori. However, in this study, an average concept based MPC is developed without such knowledge. MPC parameters are tuned over an urban drive cycle; whereas, the robustness of this MPC is tested under different drive cycles (e.g. highway and combined). Analysis shows that, the presented MPC has a comparable performance as the prescient MPC regarding fuel consumption, which assumes knows the drive cycle beforehand. Meanwhile, with the help of the proposed MPC and RAPS, the service vehicle saves up to 9% of the total fuel consumption. The proposed MPC is independent of powertrain topology such that it can be directly extended to other types of hybrid electric vehicles (HEVs), and it provides a way to apply the MPC even though future driving information is unavailable.