We search for the decay B-s(0) -> gamma gamma and measure the branching fraction for B-s(0) -> phi gamma using 121.4 fb(-1) of data collected at the Upsilon(5S) resonance with the Belle detector at the KEKB asymmetric- energy e(+)e(-) collider. The B-s(0) -> phi gamma branching fraction is measured to be (3.6 +/- 0.5(stat) +/- 0.3(syst) +/- 0.6(f(s))) x 10(-5), where f(s) is the fraction of B-s(()*())(B) over barB(s)(()*()) in b (b) over bar events. Our result is in good agreement with the theoretical predictions as well as with a recent measurement from LHCb. We observe no statistically significant signal for the decay B-s(0) -> gamma gamma and set a 90% confidence- level upper limit on its branching fraction at 3.1 x 10(-6). This constitutes a significant improvement over the previous result.