Wide usage of vehicle's onboard navigation system offers vehicles better terms to improve energy efficiency. In this paper, a computationally effective energy management strategy using model predictive control (MPC) is proposed to find the energy optimal torque split, gear shift, and velocity control of a parallel hybrid electric vehicle (HEV). We consider the vehicles in urban driving, where the vehicle trajectory is constrained by the infrastructure (road signs) and other vehicles (traffic). Restricted by the discrete gear ratio, nonlinear dynamics of the vehicles, and especially different time scales between velocity trajectory and torque split optimization, finding these control variables in one optimal problem is quite challenging. Thus, this paper uses bi-level methodology to reduce computational time and simplify the hybrid optimal problem by decoupling its components into two subproblems. In the outer loop, the optimal velocity trajectory is obtained by solving a nonlinear time-varying optimal problem using a Krylov subspace method to improve computational efficiency. In the second subproblem, we provide an explicit solution of the optimal torque split ratio and gear shift schedule by combining Pontryagin's minimum principle and numerical methods in the framework of MPC. Simulation results on an AMESim model of an HEV with seven-speed automated manual transmission over multiple driving cycles are presented. The results indicate that both energy efficiency and computational speed are improved.