Searching for new two-dimensional (2D) Dirac cone materials has been popular since the exfoliation of graphene. Herein, based on density functional theory, we predict a novel family of 2D Dirac cone materials in square transition-metal carbides MC6 (M = Mo, W) which show inherent stability confirmed by phonon spectrum analysis and ab initio molecular dynamics calculations. The Dirac point, located exactly at the Fermi level, mainly arises from the hybridization of M-dz2,x2-y2 and C-pz orbitals which gives rise to an ultrahigh Fermi velocity comparable to that of graphene. Moreover, strong spin-orbit coupling related to M-d electrons can generate large band gaps of 35 and 89 meV for MoC6 and WC6 monolayers, respectively, which allows MC6 materials to be operable at room temperature (26 meV), as candidates for nanoelectronics in the upcoming post-silicon era. The conceived novel stable metal-carbon framework materials provide a platform for designing 2D Dirac cone materials.