In this paper, we introduce and investigate a new subclass of the function class Σ of bi-univalent functions defined in the open unit disk, which are associated with the Hurwitz-Lerch zeta function, satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in this new subclass. Several (known or new) consequences of the results are also pointed out. © 2015 Academic Publications, Ltd.