ZrCo alloy exhibits distinct advantages in the storage of hydrogen and its isotopes. In this study, the phonon dispersion relation of ZrCo and ZrCoMx (M = H, D, T) is calculated. Subsequently, the thermodynamic properties of ZrCo and ZrCoMx compounds are investigated. Furthermore, an analysis is conducted on the temperature-dependent variations in the thermodynamic properties during hydrogen (deuterium, tritium) absorption reactions. Additionally, the impact of Ta doping (Zr0·875Ta0·125Co) on the thermodynamics of hydrogen storage (deuterium tritium) in ZrCo is discussed. The results indicate that H in the octahedral void leads to a higher thermodynamic value and a more stable system compared to H in the tetrahedral interstice. When ZrCo alloy store deuterium and tritium, there is an increase in ZPE, △H and △G of the system. At 300 K, the △H of ZrCo reacting with hydrogen, deuterium and tritium to form ZrCoM3 (M = H, D and T) are 85.94 kJ/mol, 90.09 kJ/mol and 92.16 kJ/mol, respectively. The ZPE and the △H of reaction are reduced upon Ta doping, thereby facilitating hydrogen (deuterium and tritium) circulating storage capabilities of alloy.