In this paper, the structural properties of TiAl3 intermetallics are investigated by the plane-wave pseudopotential density functional theory method. The calculated results are consistent with experimental and other theoretical ones. Through the quasi-harmonic Debye model we calculate the thermodynamic properties and obtain the dependences of relative volume V/V0 on pressure P and temperture T, as well as the thermal expansion and specific heat coefficients under different temperatures and pressures. For the calculated results of TiAl, we find that the increase rate of thermal expansion coefficient of TiAl under the increase of temperature is higher than that of TiAl3, and further, the effect of temperature weakens with the increase of pressure. The specific heat of TiAl3 is nearly twice that of TiAl.