This paper deals with the energy management strategy (EMS) for an on-board semi-active hybrid energy storage system (HESS) composed of a Li-ion battery (LiB) and ultracapacitor (UC). Considering both the nonlinearity of the semi-active structure and driving condition uncertainty, while ensuring HESS operation within constraints, an adaptive model predictive control (AMPC) method is adopted to design the EMS. Within AMPC, LiB Ah-throughput is minimized online to extend its life. The proposed AMPC determines the optimal control action by solving a quadratic programming (QP) problem at each control interval, in which the QP solver receives control-oriented model matrices and current states for calculation. The control-oriented model is constructed by linearizing HESS online to approximate the original nonlinear model. Besides, a time-varying Kalman filter (TVKF) is introduced as the estimator to improve the state estimation accuracy. At the same time, sampling time, prediction horizon and scaling factors of AMPC are determined through simulation. Compared with standard MPC, TVKF reduces the estimation error by 1~3 orders of magnitude, and AMPC reduces LiB Ah-throughput by 4.3% under Urban Dynamometer Driving Schedule (UDDS) driving cycle condition, indicating superior model adaptivity. Furthermore, LiB Ah-throughput of AMPC under various classical driving cycles differs from that of dynamic programming by an average of 6.5% and reduces by an average of 10.6% compared to rule-based strategy of LiB Ah-throughput, showing excellent adaptation to driving condition uncertainty.