Unmanned aerial vehicles (UAVs) are finding their way into offshore applications. In this work, we postulate an original system that entails a marine locomotive quadrotor UAV that manipulates the velocity of a floating buoy by means of a cable. By leveraging the advantages of UAVs relative to high speed, maneuverability, ease of deployment, and wide field of vision, the proposed UAV−buoy system paves the way in front of a variety of novel applications. The dynamic model that couples the buoy, UAV, cable, and water environment is presented using the Euler-Lagrange method. A stable control system design is proposed to manipulate the forward-surge speed of the buoy under two constraints: maintaining the cable in a taut state, and keeping the buoy in contact with the water surface. Polar coordinates are used in the controller design process to attain correlated effects on the tracking performance, whereby each control channel independently affects one control parameter. This results in improved performance over traditional Cartesian-based velocity controllers, as demonstrated via numerical simulations in wave-free and wavy seas.