Ti50Pd50 alloy exhibits thermoelastic martensitic phase transformation above 823 K and has the potential for high temperature shape memory material applications. Previous studies showed that this alloy is mechanically unstable with a negative C’ at room temperature. A systematic investigation of the structural, thermodynamic, electronic and elastic properties of TiPdOs is conducted using a first-principles calculation based on density functional theory. The calculated heats of formation show that this compound is thermodynamically stable as Os content is increased. It is found that an increase in Os content stabilizes the TiPd with a positive Cx2032; observed above 18.25 at. %. An increase in Os content results in an increase of the Bulk modulus and Young’s modulus above 18.25 at. %. Anisotropy factor and Vickers hardness are studied and hardness is found to increase with an increase in Os content. The results suggest that the stability of the B2 phase can be significantly enhanced by the addition of Os in TiPd alloy. These findings have important applications for future materials design in aerospace industries.