We present a model predictive control strategy for trajectory-keeping and attitude stabilization of an unmanned quadrotor. We build a controlled quadrotor model which includes motor dynamics with normal remote control inputs, and then design a linear extended-state observer based on the information extracted from the model. We use the observer to estimate external gust disturbance. The estimated values are used as compensation online by adjusting control input. As a result, the capacity of resisting disturbance can be achieved in trajectory-keeping. We propose Laguerre networks to capture the future control sequence, thereby resulting in a low computational burden. The controller is validated through a hardware-in-the-loop simulation, which shows that the controller has satisfactory control and computing performance that can meet the needs of practical engineering.