A novel neural network (NN)-based parallel model predictive control (PMPC) method is proposed to deal with the tracking problem of the quadrotor unmanned aerial vehicles (Q-UAVs) system in this article. It is well known that the dynamics of Q-UAVs are changeable while the system is operating in some specific environments. In this case, traditional NN-based MPC methods are not applicable because their model networks are pre-trained and kept constant throughout the process. To solve this problem, we propose the PMPC algorithm, which introduces parallel control structure and experience pool replay technology into the MPC method. In this algorithm, an NN-based artificial system runs in parallel with the UAV system to reconstruct its dynamics model. Furthermore, the experience replay technology is used to maintain the accuracy of the reconstructed model, so as to ensure the effectiveness of the model prediction algorithm. Furthermore, a convergence proof of the artificial system is also given in this paper. Finally, numerical results and analysis are given to demonstrate the effectiveness of the PMPC algorithm.