Manufacturing three-dimensional (3D) objects with polymers/bioceramic composite materials has been investigated in recent years. In this study, we manufactured and evaluated solvent-free polycaprolactone (PCL) and beta-tricalcium phosphate (β-TCP) composite fiber as a scaffold material for 3D printing. To investigate the optimal ratio of feedstock material for 3D printing, the physical and biological characteristics of four different ratios of β-TCP compounds mixed with PCL were investigated. PCL/β-TCP ratios of 0 wt.%, 10 wt.%, 20 wt.%, and 30 wt.% were fabricated, with PCL melted at 65 °C and blended with β-TCP with no solvent added during the fabrication process. Electron microscopy revealed an even distribution of β-TCP in the PCL fibers, while Fourier transform infrared spectroscopy demonstrated that the biomaterial compounds remained intact after the heating and manufacturing process. In addition, adding 20% β-TCP into the PCL/β-TCP mixture significantly increased hardness and Young’s Modulus by 10% and 26.5%, respectively, suggesting that PCL-20 has better resistance to deformation under load. Cell viability, alkaline phosphatase (ALPase) activity, osteogenic gene expression, and mineralization were also observed to increase according to the amount of β-TCP added. Cell viability and ALPase activity were 20% higher with PCL-30, while upregulation for osteoblast-related gene expression was better with PCL-20. In conclusion, PCL-20 and PCL-30 fibers fabricated without solvent exhibited excellent mechanical properties, high biocompatibility, and high osteogenic ability, making them promising materials for 3D printing customized bone scaffolds promptly, sustainably, and cost-effectively.