The structural, electronic, elastic and thermodynamic properties of [Formula: see text] ([Formula: see text], Al, Ga, In and TI; [Formula: see text] and N) phase have been systematically investigated by the first principles. The optimized lattice parameters are in good agreement with the experimental values and better than the available theoretical data. We calculated the elastic constants [Formula: see text] and the total density of states, which verified mechanical stability and electronic structural stability, respectively. The other elastic parameters including bulk modulus, shear modulus, Young’s modulus, Cauchy pressure, shear anisotropy factor, linear compressibility coefficients, Pugh’s ratio, Poissons’s ratio, microhardness parameter and machinability index are calculated and discussed in this work. The results show that the compounds we studied are stable in mechanics and are anisotropic materials; the compressibility along [Formula: see text]-axis is lower than that along [Formula: see text]-direction except for [Formula: see text] ([Formula: see text] and N); the compounds of [Formula: see text] ([Formula: see text]) and [Formula: see text] ([Formula: see text]) are brittle in nature, and [Formula: see text] and V2TIN are ductile in nature; the shear modulus [Formula: see text] limits the mechanical stability of the materials under consideration; the ability to resist shape change and the stiffness of [Formula: see text] are stronger compared with [Formula: see text] when A takes B, Al, Ga, In, TI, respectively. Finally we have estimated the Vickers hardness which shows that the hardness of the [Formula: see text] ([Formula: see text], Al, Ga, In, TI) would decrease when C is replaced by N. At last, we investigated the thermodynamic properties of [Formula: see text] by calculating the phonon dispersion, Debye temperature and minimum thermal conductivity. The results show that all structures are dynamical stable and the compounds of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are candidates for thermal barrier coating (TBC) materials.