In this article, we use the (M,N)-Lucas polynomials to define a new family HΣ(λ; x) of normalized holomorphic and bi-univalent functions and to establish the bounds for |a2| and |a3|, where a2, a3 are the initial Taylor-Maclaurin coefficients. Further we investigate Fekete-Szegö inequality for functions in the family HΣ(λ; x) which we have introduced here.