In this article, the performance of the sliding mode control (SMC) that is combined with the backpropagation neural network (NN) as the main control of quadrotor’s dynamic systems was examined on various trajectories and conditions, through numerical simulation. The simulation is conducted with three different trajectories in the absence and presence of the time-varying external disturbances that were adopted from previous studies. The time-varying external disturbances are implemented for the roll, pitch, yaw, and altitude movement simultaneously with the gain set up at the value of 0.8. The simulation results show that the SMC-NN scheme was able to control the quadrotor either in the absence or in the presence of time-varying external disturbances, for each trajectory without any chattering or vibration issues in the quadrotor’s dynamic system. It can be concluded that the SMC-NN is one of the control strategies that are appropriate for the mission with various conditions and circumstances.