Three-dimensional (3D) bioprinting is a family of enabling technologies that can be used to manufacture human organs with predefined hierarchical structures, material constituents and physiological functions. The main objective of these technologies is to produce high-throughput and/or customized organ substitutes (or bioartificial organs) with heterogeneous cell types or stem cells along with other biomaterials that are able to repair, replace or restore the defect/failure counterparts. Gelatin-based hydrogels, such as gelatin/fibrinogen, gelatin/hyaluronan and gelatin/alginate/fibrinogen, have unique features in organ 3D bioprinting technologies. This article is an overview of the intrinsic/extrinsic properties of the gelatin-based hydrogels in organ 3D bioprinting areas with advanced technologies, theories and principles. The state of the art of the physical/chemical crosslinking methods of the gelatin-based hydrogels being used to overcome the weak mechanical properties is highlighted. A multicellular model made from adipose-derived stem cell proliferation and differentiation in the predefined 3D constructs is emphasized. Multi-nozzle extrusion-based organ 3D bioprinting technologies have the distinguished potential to eventually manufacture implantable bioartificial organs for purposes such as customized organ restoration, high-throughput drug screening and metabolic syndrome model establishment.