We investigate for the first time the effects of a warm dark matter (WDM) power spectrum on the statistical properties of galaxies using a semi-analytic model of galaxy formation. The WDM spectrum we adopt as a reference case is suppressed – compared to the standard cold dark matter (CDM) case – below a cut-off scale ≈1 Mpc corresponding (for thermal relic WDM particles) to a mass mX= 0.75 keV. This ensures consistency with present bounds provided by the microwave background Wilkinson Microwave Anisotropy Probe data and by the comparison of hydrodynamical N-body simulations with observed Lyman-α forest. We run our fiducial semi-analytic model with such a WDM spectrum to derive galaxy luminosity functions (in B, UV and K bands) and the stellar mass distributions over a wide range of cosmic epochs, to compare with recent observations and with the results in the CDM case. The predicted colour distribution of galaxies in the WDM model is also checked against the data. When compared with the standard CDM case, the luminosity and stellar mass distributions we obtain assuming a WDM spectrum are characterized by (i) flattening of the faint-end slope and (ii) sharpening of the cut-off at the bright end for z≲ 0.8. We discuss how the former result is directly related to the smaller number of low-mass haloes collapsing in the WDM scenario, while the latter is related to the smaller number of satellite galaxies accumulating in massive haloes at a low redshift, thus suppressing the accretion of small lumps on the central, massive galaxies. These results shows how adopting a WDM power spectrum may contribute to solving two major problems of CDM galaxy formation scenarios, namely, the excess of predicted faint (low-mass) galaxies at low and – most of all – high redshifts, and the excess of bright (massive) galaxies at low redshifts.