Hybrid electric propulsion systems have been identified as the feasible solutions for regional jets and narrowbody aircraft to reduce block fuel burn, emissions, and operating cost. Different from land-based vehicles, weight is a major consideration for air transport due to weight-related lift-induced drag penalty. Thus, energy onboard balance, variation in aircraft mass during flight and the aerodynamics-propulsion coupling effects should be considered in hybrid electric aircraft energy management strategy (EMS) while satisfying aircraft maximum take-off weight constraints. In this paper, a Nonlinear Model Predictive Control based optimal energy management scheme (MPC-EMS) has been proposed to minimize the block fuel burn during flight. Firstly, the Artificial Neural Network (ANN) model is adopted with back-propagation algorithm to predict turbofan engine performance with high accuracy and computational efficiency, meanwhile gas turbine-electrical powertrain coupling effects are investigated and analysed for typical operating conditions. Then, by combining a point-mass aircraft dynamic model, nonlinear model predictive control with Cross-Entropy Method (CEM) is proposed to obtain optimal energy management based on a fully coupled aerodynamicspropulsion hybrid electric aircraft model. Besides, this state-constrained optimal control problem is re-formulated as a state-unconstrained problem with penalty function to reduce the computational load. Finally, the proposed MPC EMS algorithm is applied to Boeing 737-800 aircraft with mechanically parallel hybrid electric propulsion configuration to minimize the block fuel burn and compared with the optimization results using global Genetic Algorithm (GA) based EMS. The simulation results indicate that the proposed MPC-EMS can significantly reduce the computational time by more than 97% while obtaining similar objectives of block fuel burn and emissions reduction.