3D bioprinting creates biological structures by layering bioinks with living cells or biomaterials. Microextrusion, a type of 3D bioprinting, uses pneumatic, piston, or screw methods to extrude bioink precisely. The reliability of 3D bioprinting depends on bioink characteristics, printing conditions, and printer accuracy. Thus, a 3D bioprinter which controls these factors effectively is essential to facilitate 3D bioprinting. In this study, we developed a high-precision 3D bioprinter system (HP-BPS) with high-accuracy 3D plotting system and a screw-based dispenser. Evaluation of reducers installed on the X and Y-axis driving systems decreased motion error by up to 97%. Geometric errors of the HP-BPS were measured using a laser interferometry system. By the application of iterative position error compensation techniques, a position accuracy within ± 2.0 μm was achieved. In the specific carboxymethyl cellulose concentrations (15 and 20%), the HP-BPS could make uncollapsed bioink struts. The HP-BPS successfully fabricated 1 × 1 mm bioscaffold with 0.2 mm struts by the design of experiments and response surface methodology. These results suggest the potential of the HP-BPS for various tissue engineering applications in soft tissue construction, such as skin and blood vessels.