In the current work, we use the (M,N)-Lucas Polynomials to introduce a new family of holo-morphic and bi-univalent functions which involve a linear combination between Bazilevič functions and β-pseudo-starlike function defined in the unit disk D and establish upper bounds for the second and third coefficients of functions belongs to this new family. Also, we discuss Fekete-Szegő problem in this new family.