In this paper, Model Predictive Control (MPC) framework is exploited to synthesize a predictive controller for a parallel Hybrid Electric Vehicle (HEV) equipped with an Automated Manual Transmission. The algorithm also controls the gear shift command, together with the power split between the engine and electric machine and the engine on-off state using the route information ahead. A non-predictive controller based on a combination of Dynamic Programming (DP) and Pontryagin's Minimum Principle (PMP) is described and taken as a benchmark control solution for optimizing the gear shift problem of the parallel HEV in terms of computational efficiency. This so-called DP-PMP control approach is then utilized in the MPC framework to realize the predictive controller for a gear shift problem in a receding horizon mode. Simulation results show that the non-predictive controller improves the fuel economy up to 35.9% and 43.5% on NEDC and FTP75 respectively when compared with a conventional vehicle. Even with a short horizon, fuel saving of the predictive controller is very close to that of the non-predictive controller with a relative difference of 0.3%. Moreover, the predictive controller can be seen as a suitable realtime implementable control candidate with a fast computation property.