This paper predicts the elastic and thermodynamic characteristics of T1B2 crystal through the method of density functional theory within the generalized gradient approximation (GGA). The five independent elastic constants (Cij), the bulk modulus (Bo), the dependence of bulk modulus (Bo) on temperature T and pressure P and the coefficient of thermal expansion (αL) at various temperatures have been evaluated and discussed. According to calculation, the bulk modulus will increase with increasing pressure while decrease with the increasing temperature. The coefficient of thermal expansion is consistent with the famous Griineisen’s law when the temperature is not too high. The obtained results agree well with the experimental and other theoretical results.