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