This paper addresses the problem of trajectory tracking of an inverted pendulum mounted on an autonomous quadrotor vehicle. The mathematical model of the quadrotor-inverted-pendulum system is first derived. Thrust and angular velocity control laws are then constructed based on the backstepping technique; the former law features an implicit bound with respect to the position error. The origin of the closed-loop system error associated with the proposed control methodology is shown to be locally asymptotically stable. Realistic simulation results are presented to validate and demonstrate the performance of our solution.