The three-dimensional Dirac semimetal (3D DSM) is a new class of material with a slew of electronic and optical properties in common with graphene, while structurally having a bulk form like real metals. In particular, the Dirac band structure of 3D DSM conferred very high optical nonlinearities much like the case for graphene. Consequently, we found that 3D DSM has respectable nonlinear plasmonic performance in comparison with graphene, while retaining the structural benefits of bulk metals, having reduced passive plasmonic losses, and is much easier to handle in fabrication facilities. 3D DSM is expected to play a strong role in providing strong optical nonlinearities for all-optical switching and at the same time offering a superior platform for nanophotonic device integration.