We report evidence for the exclusive two-body charmless hadronic B meson decay B-->eta'pi, and improved measurements of B-->eta'K. The results are obtained from a data sample of 386x10(6) BB pairs collected at the Upsilon(4S) resonance, with the Belle detector at the KEKB asymmetric-energy e+e- collider. We measure B(B+-->eta'pi+)=[1.76(-0.62)(+0.67)(stat)(-0.14)(+0.15)(syst)]x10(-6) and B(B0-->eta'pi0)=[2.79(-0.96)(+1.02)(stat)(-0.34)(+0.25)(syst)]x10(-6). We also find the ratio of B(B+-->eta'K+)/B(B0-->eta'K0)=1.17+/-0.08(stat)+/-0.03(syst) and measure the direct CP asymmetries for the charged modes.