The control of quadrotor Unmanned Aerial Vehicles (UAVs) in unknown environments has become a vital approach to enable the quadrotor’s smooth movement. It is challenging for quadrotor UAVs to implement path-tracking tasks considering the random disturbance caused by unpredictable wind. In this paper, a data-driven system identification technique has been combined with the model predictive control (MPC) to enable the UAV to move back to the desired trajectory quickly upon facing the disturbance. In detail, sparse identification of nonlinear dynamics (SINDy) infers the system’s dynamical model based on time-series measurements without the need for prior knowledge of the system’s physical dynamics. A comparison has been given between the MPC-based controller and the MPC-Sindy-based controller to prove the necessity of employing Sindy on the traditional controller.