[en] We present the results of a search for the radiative decay B→Kη^'γ and find evidence for B⁺→K⁺η^'γ decays at the 3.3 standard deviation level with a partial branching fraction of (3.6±1.2±0.4)x10^-6, where the first error is statistical and the second systematic. This measurement is restricted to the region of combined Kη^' invariant mass less than 3.4 GeV/c². A 90% confidence level upper limit of 6.4x10^-6 is obtained for the partial branching fraction of the decay B⁰→K⁰η^'γ in the same Kη^' invariant mass region. These results are obtained from a 605 fb^-1 data sample containing 657x10⁶BB pairs collected at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e⁺e^- collider.