Long gamma-ray bursts (LGRBs) are associated with massive stars and are therefore linked to star formation. To reach our goal we use the Swift/BAT6 complete sample of LGRBs. In this first paper, we build the spectral energy distribution (SED) of the 14 z < 1 host galaxies of the BAT6 LGRB sample and determine their stellar masses (M) from SED fitting. To investigate the presence of a bias in the LGRB-star formation relation we compare the stellar mass distribution of the LGRB host galaxies (i) with star-forming galaxies observed in deep surveys (U1traVISTA) within the same redshift limit; (ii) with semi-analytical models of the z < 1 star-forming galaxy population; and (iii) with dedicated numerical simulations of LGRB hosts having different metallicity thresholds for the progenitor star environment. We find that at z < 1, LGRBs tend to avoid massive galaxies and are very powerful for selecting a population of faint low-mass star-forming galaxies, partly below the completeness limits of galaxy surveys.