For the problem that how to accurately estimate the unknown model and disturbance of the system in model free control, a model-free RBF neural network sliding mode controller(HODRBFSMC) based on a high-order-differentiator(HOD)is proposed. Firstly, the HOD is introduced to estimate the state variables of each order of the system model. The unknown items of the system model and external disturbances are unified as total disturbances, and the total disturbances are estimated by the RBF neural network. According to the Lyapunov theorem, the closed-loop stability of the designed controller is proved. In order to verify the effectiveness of the controller, the designed controller is applied to the trajectory control of the quadrotor to solve the problem of complex model parameters and susceptibility to external interference during flight. The simulation experiments show that the proposed method can effectively estimate and compensate the total disturbances, and its trajectory tracking ability and anti-disturbance performance are superior to PID and high-order-differentaitor feedback control(HODFC), and can well meet the needs of quadrotor control.