In this paper, we introduce and investigate a new subclass of the function class $$\Sigma $$ 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 $$|a_{2}|$$ and $$|a_{3}|$$ for functions in the new subclass introduced here. Several (known or new) consequences of the results are also pointed out. Further we obtain Fekete–Szego inequality for the new function class.