The intriguing Dirac cones in honeycomb graphene have motivated the search for novel two-dimensional (2D) Dirac materials. Based on density functional theory and the global particle-swarm optimization method, herein, we predict a new family of 2D materials in honeycomb transition-metal carbides M3C2 (M = Zn, Cd and Hg) with intrinsic Dirac cones. The M3C2 monolayer is a kinetically stable state with a linear geometry (CMC), which to date has not been observed in other transition-metal-based 2D materials. The intrinsic Dirac cones in the Zn3C2, Cd3C2 and Hg3C2 monolayers arise from p-d band hybridizations. Importantly, the Hg3C2 monolayer is a room-temperature 2D topological insulator with a sizable energy gap of 44.3 meV. When an external strain is applied, additional phases with node-line semimetal states emerge in the M3C2 monolayer. These novel stable transition-metal-carbon-framework materials hold great promise for 2D electronic device applications.