A new strategy is proposed for preparation of continuous fibre reinforced cellular structural composites (CFRCSCs) based on a fused filament fabrication. This method can endow some continuous fibers in cellular structure with good orientations by well design of fiber printing path and reconfiguration of extrusion, and can distribute fibers evenly and interleave fibers uniformly in the structure. The printed cellular structure is able to display predictable and reasonable tensile properties. In this work, the influences of printing paths, factors and structure parameters on the tensile properties of diamond shape of CFRCSCs were investigated, with which of the results to optimize the printing path and scheme for CFRCSCs. The results showed that the structural parameters like cell length affected the tensile properties greatly by variation of fiber orientations along the stretching direction. The printing parameters such as the thickness of each printed layer had a significant impact on the fiber content of CFRCSCs. An increase of the fiber content gave rise to a higher tensile property of CFRCSCs. This printing strategy provides significant references for preparation and application of high-performance composites with more complex while lightweight 3D structures.