We propose that the hexagonal crystal form of MoC is a stable and new type of topological semimetal.It hosts an exotic Fermi surface consisting of two concentric nodal rings in the presence of spin-orbit coupling,and possesses four pairs of triply degenerate points (TDPs) in the vicinity of the Fermi energy.The coexistence of the nodal ring Fermi surface and TDPs in MoC leads to extraordinary properties such as distinguishable drumhead surface states and manipulatable new fermions,which make MoC a fertile platform for in-depth understanding of topological phenomena and a potential candidate material for topological electronic devices.