A search for the lepton-flavor violating decays B^{+}→K^{+}μ^{±}e^{∓} is performed using a sample of proton-proton collision data, collected with the LHCb experiment at center-of-mass energies of 7 and 8 TeV and corresponding to an integrated luminosity of 3 fb^{-1}. No significant signal is observed, and upper limits on the branching fractions are set as B(B^{+}→K^{+}μ^{-}e^{+})<7.0(9.5)×10^{-9} and B(B^{+}→K^{+}μ^{+}e^{-})<6.4(8.8)×10^{-9} at 90% (95)% confidence level. The results improve the current best limits on these decays by more than one order of magnitude.