We study electron correlations and their impact on magnetic properties of vanadium by a combination of density functional and dynamical mean-field theory. The calculated uniform magnetic susceptibility is of Pauli type at low temperatures, while it obeys the Curie-Weiss law at higher temperatures in a qualitative agreement with experimental data. Our results for local spin-spin correlation function and local susceptibility reveal that the Curie-Weiss behaviour occurs due to partial formation of local magnetic moments. We show that these moments originate from t 2g states and their formation is mainly governed by local spin correlations caused by Hund's rule coupling. The formation of local moments is accompanied by a deviation from the Fermi-liquid behaviour although fermionic quasiparticles remain well-defined. The obtained quasiparticle mass enhancement factor of about 1.5-2 corresponds to a moderately correlated metal. By analyzing the momentum dependence of static magnetic susceptibility, we find incommensurate magnetic correlations which may cause the loss of quasiparticle coherence upon heating.