A study of the decays Bs0→μ+μ- and B0→μ+μ- has been performed using data corresponding to an integrated luminosity of 25 fb -1 of 7 and 8 TeV proton–proton collisions collected with the ATLAS detector during the LHC Run 1. For the B0 dimuon decay, an upper limit on the branching fraction is set at B(B0→μ+μ-)<4.2×10-10 at 95 % confidence level. For Bs0 , the branching fraction B(Bs0→μ+μ-)=0.9-0.8+1.1×10-9 is measured. The results are consistent with the Standard Model expectation with a p value of 4.8 %, corresponding to 2.0 standard deviations.