The electronic structures, elastic and thermodynamic properties of TiNi、Ti2Ni and TiNi3 intermetallic compounds have been investigated by first–principles scheme. The calculation results show that TiNi3 intermetallic compound has the strongest alloying ability and the highest thermodynamic stability. The thermodynamic stability sequence of these three compounds is as TiNi3 >TiNi>Ti2Ni. Their elastic properties implies that the fracture resistance of TiNi3 is better than that of the TiNi and Ti2Ni compound while the elastic anisotropy index of TiNi is the largest. Their ductile characterization comes mainly from the contribution of Ti–3d and Ni–3d orbitals as well as the orbital’s hybridization. The analysis of crystal orbital Hamilton population (COHP) also shows that the interaction between Ti–3d and Ni–3d orbitals has a dominating contribution. The thermodynamic properties show that Debye temperature of TiNi3 is higher than the others, implying a stronger bonding force among atoms in TiNi3 compound, and the minimum thermal conductivity has the same trend like Debye temperature. The entropy and internal energy increase continuously while the specific heat increased sharply in the lower temperature and almost maintains a constant after the temperature elevated to about 300 K.