Mechanical and physical properties of TiAl-base alloy are dependent on its microstructure. Therefore it is important to control the microstructure. To control of its microstructure, it is necessary to understanding and determine an accurate phase diagram. There are two methods of studying phase diagram; one is the experimental method and the other is thermodynamic calculation using a computer technique. In this study, the ternary interaction parameters of the Ti-Al-X (X=Cr, Mo, Nb) systems have been optimized using of the available ternary experimental data. The phase of liquid, α-hcp, β-bcc, γ-TiAl, $α_2-Ti_3Al$ and intermetallic compounds have been considered. The excess Gibbs energy of binary disordered phase is described by the Redlich-Kister equation. The Muggianu method is used to extrapolate the thermodynamic values of the binary systems into ternary system. The Gibbs energy of ordered phase is described by the sub-lattice model. Ti-Al-Cr, Ti-Al-Mo, Ti-Al-Nb, Ti-Al-Cr-Nb phase diagrams are calculated, which are in reasonable agreements with the experimental data. The three phase bcc+hcp+TiAl coexisting region shifts to the Al rich and χ rich side with increasing temperature. Cr, Mo, Nb are β stabilizer elements and Mo is the strongest β stabilizer element. The content of Cr increases the position of phase boundary α/α+γ shift to the Al rich side.
