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[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.