Context : The fundamental properties of brown dwarfs evolve with age . Models describing the evolution of luminosities and effective temperatures , among other physical parameters , can be empirically constrained using brown dwarfs of various masses in star clusters of well determined age and metallicity . Aims : We aim to carry out a spectroscopic and photometric characterization of low-mass brown dwarfs of the \sim 120 Myr old Pleiades open cluster . Methods : We obtained low-resolution near-infrared spectra of the J = 17.4–18.8 mag candidate L-type brown dwarfs PLIZ~28 and 35 , BRB~17 , 21 , 23 , and 29 , which are Pleiades members by photometry and proper motion . We also obtained spectra of the well-known J = 15.4–16.1 mag late M-type cluster members PPl~1 , Teide~1 , and Calar~3 . Results : We find that the former six objects have early- to mid-L spectral types and confirm previously reported M-types for the other three objects . The spectra of the L0-type BRB 17 and PLIZ 28 present a triangular H -band continuum shape , indicating that this peculiar spectral feature persists until at least the age of the Pleiades . We add to our sample 36 reported M5–L0-type cluster members , collecting their I _ { C } - and UKIDSS ZYJHK -band photometry . We confirm a possible interleaving of the Pleiades and field L-type sequences in the JHK absolute magnitude versus spectral type diagrams , and quantify marginally redder Pleiades J - K colours , by 0.11 \pm 0.20 mag , possibly related to both reddening and youth . Using field dwarf bolometric correction – and effective temperature – spectral type relations , we obtain the Hertzsprung–Russell diagram of the Pleiades sample . Theoretical models reproduce well the spectral sequence at M5.5–9 , but appear to overestimate the luminosity or underestimate the effective temperature at L0–5 . Conclusions : We classify six faint Pleiades brown dwarfs as early to mid L-type objects using low-resolution near-infrared spectra . We compare their properties to field dwarfs and theoretical models and estimate their masses to be in the range 0.025–0.035 M _ { \odot } .