Structural, magnetic, electronic and thermodynamic properties of the hexagonal U3ZrSb5 are theoretically investigated by using the full potential linearized augmented plane wave plus local orbital’s (FP-LAPW+lo) method. The exchange–correlation potential was treated with the generalized gradient approximation GGA of Wu and Cohen. Moreover, the GGA+U approximation (where U is the Hubbard correlation terms) is employed to treat the f electrons properly. The calculated structural parameters are in good agreement with the experimental data. The magnetic study reveals that U3ZrSb5 is a ferromagnetic material. Furthermore, we present a comparative study between the band structures, electronic structures, total and partial densities of states and local moments calculated within both GGA and GGA+U schemes. Our band structure calculations show the metallic behavior of this ferromagnetic compound. The thermodynamic properties are predicted through the quasi-harmonic Debye model, in which the lattice vibrations are taken into account. The variation of relative change in volume, heat capacities and the Debye temperature with temperature and pressure are successfully achieved.