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 Sălăgean type q-difference operator and satisfy some subordination conditions. Furthermore, we find estimates on the Taylor–Maclaurin coefficients | a2| and | a3| for functions in the new subclass introduced here. Several (known or new) consequences of the results are also pointed out. Further we obtain Fekete–Szegö inequality for the new function class. © 2019, African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature.