Measurements of the per-event charged-particle yield as a function of the charged-particle transverse momentum and rapidity are performed using p + Pbcollision data collected by the ATLAS experiment at the LHC at a centre-of-mass energy of root sNN= 5.02 TeV. Charged particles are reconstructed over pseudorapidity |eta| < 2.3and transverse momentum between 0.1GeVand 22GeVin a dataset corresponding to an integrated luminosity of 1 mu b(-1). The results are presented in the form of chargedparticle nuclear modification factors, where the p + Pbcharged-particle multiplicities are compared between central and peripheral p + Pbcollisions as well as to charged-particle cross sections measured in ppcollisions. The p + Pbcollision centrality is characterized by the total transverse energy measured in -4.9<eta<-3.1, which is in the direction of the outgoing lead beam. Three different estimations of the number of nucleons participating in the p + Pbcollision 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. Abroad peak is observed for all centralities and rapidities in the nuclear modification factors for chargedparticle transverse momentum values around 3GeV. The magnitude of the peak increases for more central collisions as well as rapidity ranges closer to the direction of the outgoing lead nucleus.