Context : Aims : We aim at identifying the least massive population of the solar metallicity , young ( 120 Myr ) , nearby ( 133.5 pc ) Pleiades star cluster with the ultimate goal of understanding the physical properties of intermediate-age , free-floating , low-mass brown dwarfs and giant planetary-mass objects , and deriving the cluster substellar mass function across the deuterium-burning mass limit at \approx 0.012 M _ { \odot } . Methods : We performed a deep photometric and astrometric J - and H -band survey covering an area of \sim 0.8 deg ^ { 2 } in the Pleiades cluster . The images with completeness and limiting magnitudes of J,H \approx 20.2 and \approx 21.5 mag were acquired \sim 9 yr apart , allowing us to derive proper motions with a typical precision of \pm 6 mas yr ^ { -1 } . For the cluster distance and age , the survey is sensitive to Pleiades members with masses in the interval \approx 0.2–0.008 M _ { \odot } . J - and H -band data were complemented with Z , K , and mid-infrared magnitudes up to 4.6 \mu m coming from the UKIRT Infrared Deep Sky Survey ( UKIDSS ) , the WISE catalog , and follow-up observations of our own . Pleiades member candidates were selected to have proper motions compatible with that of the cluster , and colors following the known Pleiades sequence in the interval J = 15.5–18.8 mag , and Z _ { UKIDSS } - J \geq 2.3 mag or Z nondetections for J > 18.8 mag . Results : We found a neat sequence of astrometric and photometric Pleiades substellar member candidates with two or more proper motion measurements and with magnitudes and masses in the intervals J = 15.5–21.2 mag and \approx 0.072–0.008 M _ { \odot } . The faintest objects show very red near- and mid-infrared colors exceeding those of field high-gravity dwarfs by \geq 0.5 mag . This agrees with the reported properties of field young L-type dwarfs and giant planets orbiting stars of ages of \sim 100 Myr . The Pleiades photometric sequence does not show any color turn-over because of the presence of photospheric methane absorption down to J = 20.3 mag , which is about 1 mag fainter than predicted by the combination of evolutionary models and colors computed from model atmospheres . The astrometric data suggest that Pleiades brown dwarfs have a proper motion dispersion of 6.4–7.5 mas yr ^ { -1 } , and are dynamically relaxed at the age of the cluster . The Pleiades mass function extends down to the deuterium burning-mass threshold , with a slope fairly similar to that of other young star clusters and stellar associations . The new discoveries may become benchmark objects for interpreting the observations of the emerging young ultracool population and giant planets around stars in the solar neighborhood . Conclusions :