This paper is concerned with the robust H2 estimation problem for a stationary linear system with time delays and parameter uncertainty residing in a polytope. Since the problem is infinite dimensional in nature, an attempt is made to develop finite dimensional methods that will minimize an upper bound of the estimation error variance. By applying a recently developed parameter dependent Lyapunov function, we present a less conservative design approach for minimizing the estimation error variance than existing results. Sufficient conditions are given in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the advantages of the proposed approach.