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A search is presented for the single production of vector-like quarks in proton-proton collisions at s√=13TeVs=13TeV. The data, corresponding to an integrated luminosity of 35.9fb−1fb−1, were recorded with the CMS experiment at the LHC. The analysis focuses on the vector-like quark decay into a top quark and a WW boson, with one muon or electron in the final state. The mass of the vector-like quark candidate is reconstructed from hadronic jets, the lepton, and the missing transverse momentum. Methods for the identification of bb quarks and of highly Lorentz boosted hadronically decaying top quarks and WW bosons are exploited in this search. No significant deviation from the standard model background expectation is observed. Exclusion limits at 95% confidence level are set on the product of the production cross section and branching fraction as a function of the vector-like quark mass, which range from 0.3 to 0.03pbpb for vector-like quark masses of 700 to 2000GeVGeV. Mass exclusion limits up to 1660GeVGeV are obtained, depending on the vector-like quark type, coupling, and decay width. These represent the most stringent exclusion limits for the single production of vector-like quarks in this channel.