In this paper, an intelligent Model Reference Adaptive Control (MRAC) based on a neural network is proposed for robust tracking control of quadrotor UAV under external disturbances and parameter variations. First, the singularity-free dynamic model of the quadrotor is developed using Newton-Quaternion formalism. Then, conventional MRAC is designed to generate training data. With the generated data, the Feed Forward Neural Network (FFNN) and Recurrent Neural Network (RNN) are trained offline to get an initial set of network parameters for position controller parameters estimation and attitude control of the quadrotor, respectively, and an online learning algorithm is developed to update those network parameters in real-time. Finally, the performance of the designed Neural network-based MRAC has been evaluated using a numerical simulation in a nominal scenario and by introducing parametric variation and external disturbances as matched and unmatched uncertainties into the system. The simulation results show that the proposed controller has a better tracking performance and disturbance rejection capability compared with the Linear Quadratic Regulator (LQR) and conventional MRAC. Furthermore, the utilized control efforts are minimal and smooth proving functional safety and economical use of the controller. Therefore, the suggested controller is feasible for real-time implementation of the quadrotor UAV.