Underactuated quadrotor unmanned aerial vehicles (UAVs) offer a viable solution for payload transportation but present significant challenges in attitude stabilization and swing suppression control. To address these issues, this study proposes a fully actuated (FA) system approach to tracking control of a quadrotor UAV with a hanging payload (HP). First, we establish the dynamic model of the quadrotor UAV HP system based on the Euler-Lagrange equation. Then, for the planar quadrotor UAV HP system, we transform its underactuated model into an FA one by leveraging the tools and concepts of the recently developed FA system approach. To mitigate system swing, we utilize a first-order filter for the payload swing angle and develop the FA control framework. Finally, we derive the closed-loop feedback system and conduct a series of numerical simulations to validate the performance of the proposed FA control framework.