First-principle investigations of the elastic, electronic and thermodynamic properties of TiC in NaCl structure under high pressure are conducted by using the plane-wave pseudopotential method and quasi-harmonic Debye model. The obtained lattice parameters, elastic constants and moduli at p=0 GPa and T=0 K are in very good agreement with the available experimental data and other theoretical results. According to the analysis of the density of states, the Ti-C bond becomes stronger with pressure increasing. The values of bulk modulus, thermal expansion coefficient, Debye temperature, entropy, Grüneisen parameter and heat capacity (CV) at different pressures and temperatures are obtained successfully by using the quasi-harmonic Debye model. The influence of pressure on bulk modulus, thermal expansion parameter and Debye temperature is greater than that of temperature. The CV decreases with the increase of pressure under the same temperature and tends to the Dulong-Petit limit at high temperature.