Let R be a σ--prime ring. An additive mapping F : R → R is called a generalized (α, α) -- derivation, if there exists a mapping g : R → R such that F (xy) = F(x)α(y) + α (x) g(y) for all x, y Є R. In this paper, some results about generalized derivation are extended to generalized (α, α) -- derivation in σ--prime ring.