Advantages such as simplicity of operation, high printing speed, and low cost are offered by conventional fused deposition modeling (FDM) three-axis 3D printers. However, fabrication is restricted to planar or nearly planar surfaces, and the interlayer mechanical properties of printed models are found to be relatively weak. To overcome these limitations, an innovative approach for printing complex structures on curved surfaces was proposed by employing a five-axis 3D printer. Firstly, a cradle-type configuration was adopted, and two additional rotational axes were integrated into a conventional three-axis printer to realize a novel five-degree-of-freedom machine. Secondly, the kinematic transformation matrix of the motion system was derived, and a continuous posture control algorithm together with a velocity compensation algorithm was integrated into a comprehensive control system. The reliability of the proposed algorithms was verified through three-dimensional modeling and motion simulation in MATLAB. Finally, experimental validation and process optimization were performed to identify the optimal printing parameters, successfully enabling the fabrication of high-quality, complex three-dimensional structures on freeform surfaces.