This research presents a novel 6-degree-of-freedom hybrid thrustered cable-suspended parallel robot (TCSPR) combining three cables with six propeller-based thrusters in a fully-actuated hexarotor configuration. This hybrid design aims to address the limitations of conventional cable-suspended parallel robots (CSPRs), which rely on the end-effector’s mass to maintain cable tension. This TCSPR leverages its fully-actuated hexarotor configuration to generate independent forces and torques, sustaining cable tension without relying solely on gravity. Combined with three cables attached to the end-effector’s center of mass for only force generation, this enables decoupled control of position and attitude, significantly enhancing control flexibility. A static wrench model is developed to evaluate the system’s motion capabilities, demonstrating the advantages of this design in achieving independent position and attitude control. The wrench-feasible workspace is analyzed, and the integration of the hexarotor is shown to further enhance it, particularly for lightweight end-effectors.