In this paper, we introduce two new subclasses of bi-univalent functions involving double zeta functions in open unit disk. The estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in these new subclasses are obtained and several (known or new) consequences of the results are also pointed out.Further Fekete-Szegö inequalities for the function class are determined. © 2015 Academic Publications, Ltd.