The double-differential inclusive jet cross section is measured as a function of jet transverse momentum p(T) and absolute rapidity vertical bar y vertical bar, using proton-proton collision data collected with the CMS experiment at the LHC, at a center-of-mass energy of root s = 2.76 TeV and corresponding to an integrated luminosity of 5.43 pb(-1). Jets are reconstructed within the pT range of 74 to 592 GeV and the rapidity range vertical bar y vertical bar < 3.0. The reconstructed jet spectrum is corrected for detector resolution. The measurements are compared to the theoretical prediction at next-to-leading-order QC Dusing different sets of parton distribution functions. This inclusive cross section measurement explores a new kinematic region and is consistent with QCD predictions.