A search for decays of the Higgs boson into a pair of new spin-zero particles, H?aa, where the a-bosons decay into a b-quark pair and a muon pair, is presented. The search uses 36.1fb-1of proton–proton collision data at vs=13 TeV recorded by the ATLAS experiment at the LHC in 2015 and 2016. No significant deviation from the Standard Model prediction is observed. Upper limits at 95% confidence level are placed on the branching ratio (sH/sSM) ×B(H?aa ?bbµµ), ranging from 1.2 ×10-4to 8.4 ×10-4in the a-boson mass range of 20–60GeV. Model-independent limits are set on the visible production cross-section times the branching ratio to the bbµµ final state for new physics, svis(X) ×B(X?bbµµ), ranging from 0.1fb to 0.73fb for mµµ between 18 and 62GeV.