In the present paper, the authors introduce and investigate two new subclasses of the function class Σ of bi-univalent analytic functions in the open unit disk Δ associated with Hohlov operator. The bounds on the coefficients |a2|, |a3| and |a4| for the functions in these new subclasses of Σ are obtained. Relevant connection of the results presented here with those obtained in earlier work are also pointed out.