This paper addresses a three-dimensional wind estimation problem for fixed-wing aircraft based on the tracking model predictive static programming which was originally proposed for trajectory tracking control. Without relying on any airflow measurement, the wind velocity is estimated by considering the wind vector as a virtual control input. The wind vector is corrected in real time so that the model output tracks the measured kinematic velocity states in a command-tracking manner. The proposed method features a closed-form solution and a fast indication of wind variations. The effectiveness of the proposed method is illustrated by numerical simulations in the presence of measurement noises.