Here, we report by first-principles calculations one new stable 2D Dirac material, Ta₂Se₃ monolayer. For this system, stable layered bulk phase exists, and exfoliation should be possible. Ta₂Se₃ monolayer is demonstrated to support two Dirac points close to the Fermi level, achieving the exotic 2D double Dirac semimetal. And like 2D single Dirac and 2D node-line semimetals, spin–orbit coupling could introduce an insulating state in this new class of 2D Dirac semimetals. Moreover, the Dirac feature in this system is layer-dependent and a metal-to-insulator transition is identified in Ta₂Se₃ when reducing the layer-thickness from bilayer to monolayer. These findings are of fundamental interests and of great importance for nanoscale device applications.