A bstract A search is presented for the pair production of heavy vector-like B quarks, primarily targeting B quark decays into a W boson and a top quark. The search is based on 36 . 1 fb −1 of pp collisions at $$ \sqrt{s}=13 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> <mml:mo>=</mml:mo> <mml:mn>13</mml:mn> </mml:math> TeV recorded in 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider. Data are analysed in the lepton-plus-jets final state, characterised by a high-transverse-momentum isolated electron or muon, large missing transverse momentum, and multiple jets, of which at least one is b -tagged. No significant deviation from the Standard Model expectation is observed. The 95% confidence level lower limit on the B mass is 1350 GeV assuming a 100% branching ratio to Wt . In the SU(2) singlet scenario, the lower mass limit is 1170 GeV. The 100% branching ratio limits are found to be also applicable to heavy vector-like X production, with charge +5/3, that decay into Wt . This search is also sensitive to a heavy vector-like B quark decaying into other final states ( Zb and Hb ) and thus mass limits on B production are set as a function of the decay branching ratios.