The purpose of this paper is to define Bi- Hom Γ-Lie algebra, Lie triple Hom Γ-derivation on Bi- Hom Γ-Lie algebra (g,[.,.]_λ,θ_1,θ_2)and Jordan triple Hom Γ-derivation on Bi-Hom Γ-Lie algebra (g,[.,.]_λ,θ_1,θ_2 ), Also to study the relation between Lie triple Hom Γ-derivation and Jordan triple Hom Γ-derivation on Bi-Hom Γ-Lie algebra (g,[.,.]_λ,θ_1,θ_2 ).