The transverse momentum (pT) distribution of primary charged particles is measured in minimum bias (non-single-diffractive) p+Pb collisions at 곥sNN=5.02 TeV with the ALICE detector at the LHC. The pT spectra measured near central rapidity in the range pT lower than 20 GeV/c and pT higher thatn 0.5 GeV/c exhibit a weak pseudorapidity dependence. The nuclear modification factor RpPb is consistent with unity for pT above 2 GeV/c. This measurement indicates that the strong suppression of hadron production at high pT observed in Pb+Pb collisions at the LHC is not due to an initial-state effect. The measurement is compared to theoretical calculations.