To inexpensively and easily obtain the subject compound free from a halide, having low viscosity and a high epoxy group concentration and useful as a toughening agent of a hardened material by epoxidizing an unsaturated fatty acid or its derivative by using peracetic acid.

(A) An unsaturated fatty acid or its derivative expressed by the formula I [R1 is a 1-10C alkyl; R2 is H, a 1-10C alkyl, an aryl, an alkenyl, a (meth)acryl or an alkoxysilyl; (m) and (n) are each 1-20] is epoxidized by using (B) peracetic acid or hydrogen peroxide. Preferably, the component A is a highly unsaturated fatty acid or its derivative obtained by purifying fish oil and the component A is epoxidized by reacting with an oxygen-containing gas in the presence of a metal compound (e.g. a nickel compound expressed by the formula II).