The deformation mechanism of titanium alloy at every stage during hot deformation was discussed, based on the characteristics of flow stress curves with discontinuous yielding. A viscoplastic constitutive model was built on the premise that the discontinuous yielding phenomenon was associated with the rapid dislocation multiplication at an early stage of yielding and the unified viscoplastic theory. In this model, the effect of deformation temperature and strain rate was considered. This model can describe the discontinuous yielding phenomenon, the slight degree of strain hardening after the low yield point and the mechanism of dynamic recrystallization when the strain achieved to the critical value where the dynamic recrystallization takes place. Applying the constitutive model to the isothermal compression of one new kind of metastable beta Ti2448 titanium alloy, the material constants in the model were identified by the GA-based global optimization method which was adopted in this paper. The relative difference between the predicted and experimental values is less than 5%, which implies that this constitutive model with high prediction based on the internal state variables can not only offer clear physical insight, but also can describe the flow behaviors of Ti2448 titanium alloy during hot deformation with discontinuous yielding. The generality of this model makes it possible to extend the theory to other titanium alloys that have discontinuous yielding phenomenon