Since the discovery of high-transition-temperature (high-T(c)) superconductivity in layered copper oxides, extensive effort has been devoted to exploring the origins of this phenomenon. A T(c) higher than 40 K (about the theoretical maximum predicted from Bardeen-Cooper-Schrieffer theory), however, has been obtained only in the copper oxide superconductors. The highest reported value for non-copper-oxide bulk superconductivity is T(c) = 39 K in MgB(2) (ref. 2). The layered rare-earth metal oxypnictides LnOFeAs (where Ln is La-Nd, Sm and Gd) are now attracting attention following the discovery of superconductivity at 26 K in the iron-based LaO(1-x)F(x)FeAs (ref. 3). Here we report the discovery of bulk superconductivity in the related compound SmFeAsO(1-x)F(x), which has a ZrCuSiAs-type structure. Resistivity and magnetization measurements reveal a transition temperature as high as 43 K. This provides a new material base for studying the origin of high-temperature superconductivity.