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At present, many experimental fast reactors have adopted alloy nuclear fuels, for example, U-Zr alloy fuels. During the neutron irradiation process, vacancies and hydrogen (H) impurity atoms can both exist in U-Zr alloy fuels. Here, first-principles density functional theory (DFT) is employed to study the behaviors of vacancies and H atoms in disordered-γ(U,Zr) as well as their impacts on the electronic structure and mechanical properties. The formation energy of vacancies and hydrogen solution energy are calculated. The effect of vacancies on the migration barrier of hydrogen atoms is revealed. The effect of vacancies and hydrogen atom on densities of states and elastic constants are also presented. The results illustrate that U vacancy is easier to be formed than Zr vacancy. The H interstitial prefers the tetrahedral site. Besides, U vacancy shows H-trap ability and can raise the H migration barrier. Almost all the defects lead to decreases in electrical conductivity and bulk modulus. It is also found that the main effect of defects is on the U-5f orbitals. This work provides a theoretical understanding of the effect of defects on the electronic and mechanical properties of U-Zr alloys, which is an essential step toward tailoring their performance.