A bstract A measurement of the production of a prompt J/ψ meson in association with a W ± boson with W ± → μν and J/ψ → μ + μ − is presented for J/ψ transverse momenta in the range 8 . 5–150 GeV and rapidity | y J/ψ | &lt; 2 . 1 using ATLAS data recorded in 2012 at the LHC. The data were taken at a proton-proton centre-of-mass energy of $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 8 TeV and correspond to an integrated luminosity of 20 . 3 fb − 1 . The ratio of the prompt J/ψ plus W ± cross-section to the inclusive W ± cross-section is presented as a differential measurement as a function of J/ψ transverse momenta and compared with theoretical predictions using different double-parton-scattering cross-sections.