Drop-on-demand (DOD) 3D bioprinting technologies currently hold the greatest promise for generating functional tissues for clinical use and for drug development. However, existing DOD 3D bioprinting technologies have three main limitations: (1) droplet volume inconsistency; (2) the ability to print only bioinks with low cell concentrations and low viscosity; and (3) problems with cell viability when dispensed under high pressure. We report our success developing a novel direct-volumetric DOD (DVDOD) 3D bioprinting technology that overcomes each of these limitations. DVDOD can produce droplets of bioink from < 10 nL in volume using a direct-volumetric mechanism with < ± 5% volumetric percent accuracy in an accurate spatially controlled manner. DVDOD has the capability of dispensing bioinks with high concentrations of cells and/or high viscosity biomaterials in either low- or high-throughput modes. The cells are subjected to a low pressure during the bioprinting process for a very short period of time that does not negatively impact cell viability. We demonstrated the functions of the bioprinter in two distinct manners: (1) by using a high-throughput drug-delivery model; and (2) by bioprinting micro-tissues using a variety of different cell types, including functional micro-tissues of bone, cancer, and induced pluripotent stem cells. Our DVDOD technology demonstrates a promising platform for generating many types of tissues and drug-delivery models.