Three-dimensional (3D) printing technology is expected to solve the organ shortage problem. However, owing to the accuracy limitations, it is difficult for the current bioprinting technology to achieve an accurate control of the spatial position and distribution of a single cell or single component droplet. In this study, to accurately achieve the directional deposition of different cells and biological materials in the spatial position for the construction of large transplantable tissues and organs, a high-precision multichannel 3D bioprinter with submicron-level motion accuracy is designed, and concurrent and synergistic printing methods are proposed. Based on the high-precision motion characteristics of the gantry structure and the requirements of concurrent and synergistic printing, a 3D bioprinting system with a set of 6 channels is designed to achieve six-in-one printing. Based on the Visual C++ environment, a control system software that integrates the programmable multi-axis controller (PMAC) motion, pneumatic, and temperature control subsystems was developed and designed. Finally, based on measurements and experiments, the 3D bioprinter and its control system was verified to fulfil the requirements of multichannel, concurrent, and synergistic printing with submicron-level motion accuracy, significantly shortening the printing time and improving the printing efficiency. This study not only provides an equipment basis for printing complex heterogeneous tissue structures, but also improves the flexibility and functionality of bioprinting, and ultimately makes the construction of complex multicellular tissues or organs possible.