A measurement is presented of the ϕ×BR(ϕ→K+K−) production cross section at s√ = 7 TeV using pp collision data corresponding to an integrated luminosity of 383 μb−1, collected with the ATLAS experiment at the LHC. Selection of ϕ(1020) mesons is based on the identification of charged kaons by their energy loss in the pixel detector. The differential cross section is measured as a function of the transverse momentum, pT,ϕ, and rapidity, yϕ, of the ϕ(1020) meson in the fiducial region 500 <pT,ϕ< 1200 MeV, |yϕ|< 0.8, kaon pT,K> 230 MeV and kaon momentum pK< 800 MeV. The integrated ϕ(1020)-meson production cross section in this fiducial range is measured to be σϕ×BR(ϕ→K+K−) = 570 ± 8 (stat) ± 66 (syst) ± 20 (lumi) μb.