We present predictions for the total cross section for the production of a charged Higgs boson in the intermediate-mass range ($mH\pm \sim mt$) at the LHC, focusing on a type-II two-Higgs-doublet model. Results are obtained at next-to-leading order (NLO) accuracy in QCD perturbation theory, by studying the full process $pp\to H\pm W\mp bb¯$ in the complex-(top)-mass scheme with massive bottom quarks. Compared to lowest-order predictions, NLO corrections have a sizeable impact: they increase the cross section by roughly 50% and reduce uncertainties due to scale variations by more than a factor of two. Our computation reliably interpolates between the low- and high-mass regime. Our results provide the first NLO prediction for charged Higgs production in the intermediate-mass range and therefore allow to have NLO accurate predictions in the full $mH\pm$ range. The extension of our results to different realisations of the two-Higgs-doublet model or to the supersymmetric case is also discussed.