Measurements of the per-event charged-particle yield as a function of the charged-particle transverse momentum and rapidity are performed using p+Pb collision data collected by the ATLAS experiment at the LHC at a centre-of-mass energy of sNN=5.02TeV . Charged particles are reconstructed over pseudorapidity |η|<2.3 and transverse momentum between 0.1 GeV and 22 GeV in a dataset corresponding to an integrated luminosity of 1 μb−1 . The results are presented in the form of charged-particle nuclear modification factors, where the p+Pb charged-particle multiplicities are compared between central and peripheral p+Pb collisions as well as to charged-particle cross sections measured in pp collisions. The p+Pb collision centrality is characterized by the total transverse energy measured in −4.9<η<−3.1 , which is in the direction of the outgoing lead beam. Three different estimations of the number of nucleons participating in the p+Pb collision are carried out using the Glauber model and two Glauber–Gribov colour-fluctuation extensions to the Glauber model. The values of the nuclear modification factors are found to vary significantly as a function of rapidity and transverse momentum. A broad peak is observed for all centralities and rapidities in the nuclear modification factors for charged-particle transverse momentum values around 3 GeV . The magnitude of the peak increases for more central collisions as well as rapidity ranges closer to the direction of the outgoing lead nucleus.