Tissue engineering has been developed with the ultimate aim of manufacturing human organs, but success has been limited to only thin tissues and tissues with no significant structures. In order to construct more complicated tissues, we have developed a three-dimensional (3D) fabrication technology in which 3D structures are directly built up by layer-by-layer printing with living cells and several tissue components. We developed a custom-made inkjet printer specially designed for this purpose. Recently, this printer was improved, and the on-demand printing mode was developed and installed to fabricate further complicated structures. As a result of this version, 3D layer-by-layer printing based on complicated image data has become possible, and several 2D and 3D structures with more complexity than before were successfully fabricated. The effectiveness of the on-demand printing mode in the fabrication of complicated 3D tissue structures was confirmed. As complicated 3D structures are essential for biofunctional tissues, inkjet 3D biofabrication has great potential for engineering complicated bio-functional tissues.