The present invention provides: a method for producing an epoxyalkane capable of obtaining an epoxide in a high yield while attaining a high olefin conversion rate and a high selectivity for epoxides even when an olefin includes a long carbon chain, and a solid oxidation catalyst. The method for producing an epoxyalkane of the present invention comprises reacting an olefin with an oxidant in the presence of a solid oxidation catalyst, wherein the solid oxidation catalyst comprises a transition metal and a carrier that supports the transition metal, and the carrier is a composite of a metal oxide with a phosphonic acid.