Inclusive jet production in pPb collisions at a nucleon–nucleon (NN) center-of-mass energy of √sNN= 5.02TeV is studied with the CMS detector at the LHC. A data sample corresponding to an integrated luminosity of 30.1 nb- 1 is analyzed. The jet transverse momentum spectra are studied in seven pseudorapidity intervals covering the range - 2.0 < ηCM< 1.5 in the NN center-of-mass frame. The jet production yields at forward and backward pseudorapidity are compared and no significant asymmetry about ηCM= 0 is observed in the measured kinematic range. The measurements in the pPb system are compared to reference jet spectra obtained by extrapolation from previous measurements in pp collisions at √s=7TeV. In all pseudorapidity ranges, nuclear modifications in inclusive jet production are found to be small, as predicted by next-to-leading order perturbative QCD calculations that incorporate nuclear effects in the parton distribution functions.