There exists still the controversy on the stable structure of Laves-phase Co<sub>2</sub>(HfTa) alloys with the C14,C15 or C36 structures.In this study,the stability,electronic and thermodynamic properties of Laves-phase Co<sub>2</sub>(HfTa) were investigated.In order to fully understand the influence of magnetic state and temperature on phase stability,we systematically study the free energy change at finite temperature,elastic stability,and phonon dispersion.The low Curie temperature could be estimated,which suggests the Co<sub>2</sub>(HfTa) alloys adopt the paramagnetic state at wide temperature range.Results indicate that the lattice vibration and electronic excitation have an important effect on the phase stability.The ground state of Co<sub>2</sub>Hf compound is C14-type structure,while the ground state of Co<sub>2</sub>Ta is a C36,without the effect of temperature.After doping Hf with different concentrations (0.25,0.50,0.75) in Co<sub>2</sub>Ta,the most stable structure still adopts the C36-type structure.After considering the contribution of vibration entropy and electron entropy,the relatively stable structures of Co<sub>2</sub>Hf and Co<sub>2</sub>Ta undergoes the C36-C14 phase transition.In addition,the thermodynamic properties,including Debye temperature,heat capacity and vibration entropy,which vary with pressure and temperature,are studied.The electronic properties of Co<sub>2</sub>Hf and Co<sub>2</sub>Ta compounds are analyzed by the charge difference and density of states.The similar electronic density of states between different phases suggest that this Lave phases have the similar stability.The Hf-Co bonding with a certain direction is revealed.Our results are of great significance for understanding the structure and properties of Co<sub>2</sub>Hf and Co<sub>2</sub>Ta compounds.