Suspended load transportation using unmanned aerial vehicles such as quadrotors is challenging if the load mass is uncertain or varies over time. This uncertain disturbance can significantly degrade the trajectory tracking performance and stability of the quadrotor system, causing transportation to be unsafe. To address this problem, a robust trajectory tracking method based on task-parameterized model predictive control is proposed. By using receptive field weighted regression algorithm, this method can online learn and update time-variant dynamic model that treat task-parameterized variables as external disturbances. Based on the updated model, model predictive control is then used to compute an optimal feedback control law for the quadrotor to robustly track a desired trajectory. Compared with traditional model predictive control, simulation results validate that the proposed method can not only achieve a more accurate trajectory tracking with a fixed load mass, but also can capture and address the sudden change of the load mass in a shorter time with a smaller trajectory deviation.