Context. In the past few decades, several tens of main belt asteroids have been found to exhibit basaltic surface composition, similar to the one of Vesta and basaltic Howardite, Eucrite, and Diogenite achondrite meteorites (HEDs). Most of these objects (V-types) belong to the Vesta dynamical family. Several questions on the relationship between Vesta, V-types, and HEDs are still unresolved. In particular, Vesta is spectroscopically bluer than most V-types. Aims. To date, it has not yet been understood whether these spectral differences are due to space weathering, similar to what has been observed for OC meteorites and S-type asteroids. To test this hypothesis, ion irradiation experiments were performed on different samples of eucrites to simulate the effects of space weathering on Vesta and V-types by solar wind ions. Methods. Eucrite meteorites were analyzed before and after different stages of ion irradiation by VIS-NIR reflectance spectroscopy (0.4-2.5 μm). We used different ions (Ar + , C + ) with different energies (from 60 to 200 keV) to weather the samples. Results. Ion irradiation was observed to alter the spectral properties of eucrite meteorites, inducing progressive reddening and darkening of the irradiated samples. Different eucrite samples (Bereba and Dar Al Gani 684) show different reddening behaviors. Because they are patchy, reddening also varied between different parts of the same meteorite. Moreover, for both meteorites, irradiation effects are much faster (∼100 times) for C + than for Ar + ions. Conclusions. Comparing the laboratory spectra of eucrites before and after different stages of ion irradiation with those of V-types, it turns out that the slope spread shown by V-type asteroids can be explained by space weathering. These results provide new clues to the connection between Vesta, V-types, and HEDs, and are also useful in the context of the NASA Dawn mission to Vesta.