This paper proposed a novel fully-actuated hexacopter. It features a dual-frame passive tilting structure and achieves independent control of translational motion and attitude with minimal actuators. Compared to previous fully-actuated UAVs, it liminates internal force cancellation, resulting in higher flight efficiency and endurance under equivalent payload conditions. Based on the dynamic model of fully-actuated hexacopter, a full-actuation controller is designed to achieve efficient and stable control. Finally, simulation is conducted, validating the superior fully-actuated motion capability of fully-actuated hexacopter and the effectiveness of the proposed control strategy.