Inclusive jet and dijet cross-sections are measured in proton-proton collisions at a centre-of-mass energy of 13 TeV. The measurement uses a dataset with an integrated luminosity of 3.2 fb(-1) recorded in 2015 with the ATLAS detector at the Large Hadron Collider. Jets are identified using the anti-lit algorithm with a radius parameter value of R = 0.4. The inclusive jet cross-sections are measured double-differentially as a function of the jet transverse momentum, covering the range from 100 GeV to 3.5 TeV, and the absolute jet rapidity up to vertical bar y vertical bar = 3. The double-differential dijet production cross-sections are presented as a function of the dijet mass, covering the range from 300 GeV to 9 TeV, and the half absolute rapidity separation between the two leading jets within vertical bar y vertical bar < 3, y*, up to y* = 3. Next-to-leading-order, and next-to-next-to-leading-order for the inclusive jet measurement, perturbative QCD calculations corrected for non-perturbative and electroweak effects are compared to the measured cross-sections.