The production cross sections for prompt charmed mesons D ⁰, D ⁺, D ^{∗ +} and Ds+ were measured at mid-rapidity in proton–proton collisions at a centre-of-mass energy s=7TeV with the ALICE detector at the Large Hadron Collider (LHC). D mesons were reconstructed from their decays D ⁰→ K ^-π⁺, D ⁺→ K ^-π⁺π⁺, D ^{∗ +}→ D ⁰π⁺, Ds++→K-K+π+, and their charge conjugates.With respect to previous measurements in the same rapidity region, the coverage in transverse momentum (p_T) is extended and the uncertainties are reduced by a factor of about two. The accuracy on the estimated total c c ¯ production cross section is likewise improved. The measured p_T-differential cross sections are compared with the results of three perturbative QCD calculations.