The jet radial structure and particle transverse momentum (p_T) composition within jets are presented in centrality-selected Pb–Pb collisions at s_NN=2.76 TeV. Track-based jets, which are also called charged jets, were reconstructed with a resolution parameter of R=0.3 at midrapidity |η_{ch jet}|<0.6 for transverse momenta p_{T,ch jet}=30–120 GeV/c. Jet–hadron correlations in relative azimuth and pseudorapidity space (Δφ,Δη) are measured to study the distribution of the associated particles around the jet axis for different p_T,assoc-ranges between 1 and 20 GeV/c. The data in Pb–Pb collisions are compared to reference distributions for pp collisions, obtained using embedded PYTHIA simulations. The number of high-p_T associate particles (4<p_T,assoc<20 GeV/c) in Pb–Pb collisions is found to be suppressed compared to the reference by 30 to 10%, depending on centrality. The radial particle distribution relative to the jet axis shows a moderate modification in Pb–Pb collisions with respect to PYTHIA. High-p_T associate particles are slightly more collimated in Pb–Pb collisions compared to the reference, while low-p_T associate particles tend to be broadened. The results, which are presented for the first time down to p_{T,ch jet}=30 GeV/c in Pb–Pb collisions, are compatible with both previous jet–hadron-related measurements from the CMS Collaboration and jet shape measurements from the ALICE Collaboration at higher p_T, and add further support for the established picture of in-medium parton energy loss.