To obtain high-performance spintronic devices with high integration density, two-dimensional (2D) half-metallic materials are highly desired. Herein, we proposed a stable 2D material, i.e., the Mg3C2 monolayer, with a honeycomb-kagome lattice based on the particle-swarm optimization algorithm and first-principles calculations. This monolayer is an anti-ferromagnetic (AFM) semiconductor in its ground state. We have also demonstrated that a transition from an AFM semiconductor to a ferromagnetic half-metal in this 2D material can be induced by carrier (electron or hole) doping. The half-metallicity arises from the 2pz orbitals of the carbon (C) atoms for the electron-doped system and from the C 2px and 2py orbitals in the case of hole doping. Our findings highlight a new promising material with controllable magnetic and electronic properties towards 2D spintronic applications.