The structural and thermodynamic properties of TiAl intermetallics under high pressure have been investigated by ab initio plane-wave pseudopotential density functional theory method. It is found that the ratio of lattice parameter c to a keeps almost constant with a value of 1.02 under the pressure from 0 to 20 GPa, which agrees well with the experimental results. With the pressure increasing from 20 to 45 GPa the values of c/a decrease almost linearly from 1.02 to 0.99. These calculated results indicate under low pressure the variation rate for a-axis is almost the same to that for c-axis, but under higher pressure the variation for a-axis is smaller than along c-axis. Through the quasi-harmonic Debye model, the equation of state (EOS) of TiAl intermetallics, as well as the thermal expansion and heat capacity at various pressures and temperatures are also studied.