A search for a heavy neutral Higgs boson, A, decaying into a Z boson and another heavy Higgs boson, H, is performed using a data sample corresponding to an integrated luminosity of 36.1 fb−1 from proton–proton collisions at s=13 TeV recorded in 2015 and 2016 by the ATLAS detector at the Large Hadron Collider. The search considers the Z boson decaying to electrons or muons and the H boson into a pair of b-quarks. No evidence for the production of an A boson is found. Considering each production process separately, the 95% confidence-level upper limits on the pp→A→ZH production cross-section times the branching ratio H→bb are in the range of 14–830 fb for the gluon–gluon fusion process and 26–570 fb for the b-associated process for the mass ranges 130–700 GeV of the H boson and 230–800 GeV of the A boson. The results are interpreted in the context of two-Higgs-doublet models.