We study electron correlations and their impact on magnetic properties of bcc vanadium by a combination of density functional and dynamical mean-field theory. The calculated uniform magnetic susceptibility in bcc structure is of Pauli type at low temperatures, while it obeys the Curie-Weiss law at higher temperatures. Thus, we qualitatively reproduce the experimental temperature dependence of magnetic susceptibility without introducing the martensitic phase transition. Our results for local spin-spin correlation function and local susceptibility reveal that the Curie-Weiss behavior appears due to partial formation of local magnetic moments, which originate from t2g states and occur due to local spin correlations caused by Hund's rule coupling. At the same time, the fermionic quasiparticles remain well defined, while the formation of local moments is accompanied by a deviation from the Fermi-liquid behavior. In particular, the self-energy of the t2g states shows the nonanalytic frequency dependence, which is a characteristic of the spin-freezing behavior, while the quasiparticle damping changes approximately linearly with temperature in the intermediate temperature range 200–700 K. By analyzing the momentum dependence of static magnetic susceptibility, we find incommensurate magnetic correlations, which may provide a mechanism for unconventional superconductivity at low temperatures.