In this paper, we introduce and investigate a new subclass of the function class Sigma of biunivalent functions defined in the open unit disk, which are associated with the S. al. agean type q-difference operator and satisfy some subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients vertical bar a(2 vertical bar) and vertical bar a(3)vertical bar 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.