The problem of trajectory tracking for quadrotor unmanned aerial vehicles (UAVs) is investigated in this paper. An iterative linear quadratic regulator (iLQR) based model predictive control (MPC) strategy is proposed. The proposed iLQR-MPC strategy solves the nonlinear optimal control problem using the iLQR algorithm and implements the control in a receding horizon manner. A constrained iLQR algorithm is designed in the framework of the augmented Lagrangian method to solve the optimization problem induced by the trajectory tracking. Finally, a comparative simulation experiment is conducted to demonstrate the effectiveness and advantage of the proposed control strategy.