The generalized fractional integral operators are shown to be bounded from an Orlicz–Hardy space (Formula presented.) to another Orlicz–Hardy space (Formula presented.), where Φ and Ψ are generalized Young functions. The result extends the boundedness of the usual fractional integral operator (Formula presented.) from (Formula presented.) to (Formula presented.) for (Formula presented.) and (Formula presented.), which was proved by Stein and Weiss in 1960.