The most widely used 3D process, fused deposition modeling (FDM), has insufficient interlayer adhesion due to its layer-by-layer forming method. A support material is also essential for the hollow parts and cantilevers. Moreover, the polymer materials used have limited mechanical properties. These issues have restricted the application of FDM in high-performance fields. Continuous fiber-reinforced thermoplastic composites (CFRTPCs) have high mechanical properties and have recently become the focus of research in the field of 3D printing. This paper, using pipe parts as an example, proposes a hybrid of pure polymer (pure PLA used) and CFRTPC (flax fiber pre-impregnated filament) material to develop a printing method based on the outstanding mechanical properties of CFRTPC material. After studying the printing path planning algorithm, the CFRTPC filament is laid along the axial and radial directions on the surface of the polymer base to improve the printed parts’ properties. The method feasibility and algorithm accuracy are verified through the development of five-axis printing equipment with a double nozzle. Through the printed sample’s tensile, compression and bending tests, the results show that the tensile, compressive and bending properties of PLA pipe can be significantly enhanced by laying CFRTPC filament along the axial and radial directions of the pipe. To summarize, the introduction of CFRTPCs greatly improved the mechanical properties of the printed parts, and the implementation of our method provides an effective way to solve the defects of the FDM process.