MXenes, which constitute a kind of graphene-like material, have been intensively investigated due to their applications in future nanoelectronics technology. These MXenes are either metallic or semiconducting, whereas Dirac cones similar to graphene have rarely been reported. Using first-principles calculations, we proposed a new MXene, namely Zr2Si, whose antiferromagnetic (AFM) ground state exhibited in these calculations anisotropic Dirac cones with Fermi velocities comparable to that in graphene. The Dirac spectrum here was determined to arise mainly from the dx2-y2 and dz2 orbitals of Zr atoms. Additionally, the Dirac cones can be gapped when taking the spin-orbit coupling (SOC) and Coulomb repulsive interaction (U) into account, which opens an avenue for using the Zr2Si MXene for electronics applications.