The differential cross-section for pair production of top quarks with high transverse momentum is measured in 20.3  fb−1 of proton-proton collisions at a center-of-mass energy of 8 TeV. The measurement is performed for tt¯ events in the lepton+jets channel. The cross-section is reported as a function of the hadronically decaying top quark transverse momentum for values above 300 GeV. The hadronically decaying top quark is reconstructed as an anti-kt jet with radius parameter R=1.0 and identified with jet substructure techniques. The observed yield is corrected for detector effects to obtain a cross-section at particle level in a fiducial region close to the event selection. A parton-level cross-section extrapolated to the full phase space is also reported for top quarks with transverse momentum above 300 GeV. The predictions of a majority of next-to-leading-order and leading-order matrix-element Monte Carlo generators are found to agree with the measured cross-sections.