In this paper, we introduce and investigate a new subclass of the function class S of bi-univalent functions defined in the open unit disk, which are associated with the Hurwitz-Lerch zeta function and satisfy some subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a.2| and |a3| for functions in the new subclass introduced here. Several (known or new) consequences of the results are also pointed out. © 2016 Allahabad Mathematical Society.