In this paper, we define a new class of bi-univalent functions of complex order $∑_{q}ⁿ(τ,ζ;φ)$ which is defined by subordination in the open unit disc $D$. By using $D_{q}ⁿϜ(ς)$ operator. Furthermore, using the Faber polynomial expansions, we get upper bounds for the coefficients of function belonging to this class.