Two-dimensional (2D) Dirac cone materials have many interesting physical properties. Therefore, people have been trying to find 2D materials with Dirac cones. Here, based on first principle calculations, we studied a new 2D Dirac cone material family MX6C2H monolayers (M = N,P,As and Sb, X = C,Si,Ge and Sn). The calculation of the cohesive energy indicated that the MX6C2H sheets have excellent energy stability. And the phonon spectrum showed their excellent dynamical stability. The electronic calculation revealed that the 2D MX6C2H monolayers have graphene-like band structures and ultra-high Fermi velocities comparable to graphene. The spin–orbit–coupling effect can open a sizable topological band gap in SbSn6C2H monolayer so that it can be effectively classified as quantum spin Hall insulators. In addition, the Dirac cone of PC6C2H monolayer can be adjusted by applying in-plane uniaxial strain, which is much easier than that of graphene. These interesting properties indicate that the novel 2D MX6C2H system has potential application value in nanoelectronics.