In this work, by using the Al-Oboudi differential operator and the rule of subordination, we introduced the new subclasses Dn,ρ Σ,δ(Φ) and Fn,α Σ,δ (Φ) of the bi-univalent functions. Likewise, we use the Fibonacci numbers to derive the initial coefficients bounds for |a2| and |a3| of the bi-univalent function subclasses.