The co-phase appears as a metastable phase in several binary, ternary, and multicomponent alloys. While formation of this phase is studied extensively in Ti-Al-Nb and Ti-Al-V systems, it has not been investigated so widely in Ti-Al-Mo alloys. The aim of the present investigation is to study the displacive B2 to co transformations in Ti3Al2Mo system by using first-principles calculations. We find that that atomic shuffles required for the transformation in Ti3Al2Mo are about half of the Ti3Al2Nb alloy. We calculate heat of formation for several compounds to understand the bonding and hybridization between the atoms and the reason behind the differences between these to systems. It is found that Ti-Nb bond is weaker than Ti-Mo while Nb-Al is much stronger than Mo-Al. The stability of B2 phase against ω-type atomic displacement is a competition between these bonds. Also by extending our calculations to finite temperature, we show that the addition of Mo will extend the ω-phase stability to higher temperature compared to Ti3Al2Nb system.