We have performed a deep, wide-field imaging survey of the Pleiades cluster (Melotte 22) in the R and I-bands to search for very low-mass stars and brown dwarfs. The survey extends over ~ 2.5 square degrees around the cluster's center down to a ~ 90% completeness limit of R ~ 23 and I ~ 22. We find 26 objects whose location in the (I, R-I) color-magnitude diagram is consistent with them being Pleiades members. Of these, 17 have extremely red (R-I) colors and low I luminosity, which make them prime brown dwarf candidates. We present the luminosity function of the Pleiades cluster down to M_I ~ 15. Using current-generation theoretical models, we compute the mass of the brown dwarf candidates which is found to range from the hydrogen-burning limit down to about 0.045MMsolar. Based on these results, a preliminary estimate of the Pleiades mass function is presented. While the stellar portion of the Pleiades mass function is well approximated by the log-normal IMF of Miller & Scalo (1979), the substellar part of it is found to be slightly higher than predicted by Miller & Scalo's IMF. In a log-log plot, the IMF is found to be still rising in the substellar domain, with a slope consistent with dN/dM ~ M(-0.6) if a power-law functional form is assumed. We estimate a total of about 250 objects below the hydrogen burning mass limit in the Pleiades which nevertheless make up only a few per cent of the mass of the cluster. Based on observations obtained at the Canada-France-Hawaii Telescope and the KPNO 4m telescope.