The computation costs of predicting flight trajectories of unmanned aircraft vehicle (UAV) can be expensive or even prohibitive especially for the large number of UAVs in UAV traffic management (UTM). This study proposes the concept of hybrid learning, a novel approach based on data-driven learning and underlying physics, as a computationally efficient method for the simulation of UAV dynamics. The hybrid learning integrates the underlying physics of UAV systems into learning models such as neural networks to reduce the training and simulation costs. The application of hybrid learning for simulating UAV dynamics is demonstrated using a recently introduced physics-aware network known as the deep residual recurrent neural network (DR-RNN) on a quadcopter model. The UAV dynamics are described using a six degrees-of-freedom model. The DR-RNN is used to predict the response of UAV under arbitrary control inputs. The results show that the DR-RNN can accurately predict UAV responses and has excellent extrapolation capabilities. Moreover, the DR-RNN exhibits superior computation efficiency compared with a classical numerical method, the first-order Runge-Kutta method, highlighting its suitability in serving as surrogate models for UAV systems.