Measurements are made of differential cross-sections of highly boosted pair-produced top quarks as a function of top-quark and tt¯ system kinematic observables using proton-proton collisions at a center-of-mass energy of s=13 TeV. The data set corresponds to an integrated luminosity of 36.1 fb−1, recorded in 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider. Events with two large-radius jets in the final state, one with transverse momentum pT>500 GeV and a second with pT>350 GeV, are used for the measurement. The top-quark candidates are separated from the multijet background using jet substructure information and association with a b-tagged jet. The measured spectra are corrected for detector effects to a particle-level fiducial phase space and a parton-level limited phase space, and are compared to several Monte Carlo simulations by means of calculated χ2 values. The cross-section for tt¯ production in the fiducial phase-space region is 292±7(stat)±71(syst) fb, to be compared to the theoretical prediction of 384±36 fb.