The jet fragmentation function of inclusive jets with transverse momentum pT above 100GeV/c in PbPb collisions has been measured using reconstructed charged particles with pT above 1GeV/c in a cone of radius 0.3 around the jet axis. A data sample of PbPb collisions collected in 2011 at a nucleon-nucleon center-of-mass energy of sNN=2.76TeV corresponding to an integrated luminosity of 150μb−1 is used. The results for PbPb collisions as a function of collision centrality and jet transverse momentum are compared to reference distributions based on pp data collected at the same center-of-mass energy in 2013, with an integrated luminosity of 5.3pb−1. A centrality-dependent modification of the fragmentation function is found. For the most central collisions, a significant enhancement is observed in the PbPb/pp fragmentation function ratio for charged particles with pT less than 3GeV/c. This enhancement is observed for all jet pT bins studied.