This article addresses the development and experimental validation of a trajectory-tracking control for a miniature autonomous Quadrotor helicopter system (X4-prototype) using a robust algorithm control based on second-order sliding mode technique or also known as super-twisting algorithm in outdoor environments. This nonlinear control strategy guarantees the convergence in finite time to a desired path r(t) in the presence of external disturbances or uncertainties in the model affecting the appropriate behavior of our Quadrotor helicopter. For this purpose, a polynomial smooth curve trajectory is selected as a reference signal where the corresponding derivatives of the function are bounded. Moreover, we consider disturbances due to wind gusts acting on the aerial vehicle, and the reference signal is pre-programmed in an advanced autopilot system. The proposed solution consists of implementing a real-time control law based on super-twisting control using GPS measurements in order to obtain the position in the xy-plane to accomplish the desired trajectory. Simulation and experimental results of trajectory-tracking control are presented to demonstrate the performance and robustness of the proposed nonlinear controller in windy conditions.