Graphene-like two-dimensional materials have garnered tremendous interest as emerging device materials for nanoelectronics due to their remarkable properties. However, their applications in spintronics have been limited by the lack of intrinsic magnetism. Here, using hybrid density functional theory, we predict ferromagnetic behavior in a graphene-like two-dimensional Cr2C crystal that belongs to the MXenes family. The ferromagnetism, arising from the itinerant Cr d electrons, introduces intrinsic half-metallicity in Cr2C MXene, with the half-metallic gap as large as 2.85 eV. We also demonstrate a ferromagnetic-antiferromagnetic transition accompanied by a metal to insulator transition in Cr2C, caused by surface functionalization with F, OH, H, or Cl groups. Moreover, the energy gap of the antiferromagnetic insulating state is controllable by changing the type of functional groups. We further point out that the localization of Cr d electrons induced by the surface functionalization is responsible for the ferromagnetic-antiferromagnetic and metal to insulator transitions. Our results highlight a new promising material with tunable magnetic and electronic properties toward nanoscale spintronics and electronics applications.