This paper is concerned with the problem of robust H-infinity filtering for linear continuous-time systems with polytopic parameter uncertainties and time-varying delay in the state. We utilize the polynomially parameter-dependent idea to solve the robust H-infinity filtering problem, with new linear matrix inequality conditions obtained for the existence of admissible filters. These conditions are developed based on homogeneous polynomially parameter-dependent matrices of arbitrary degree. The delay-dependence and polynomial parameter-dependence guarantee the proposed approach to be potentially less conservative, which is shown via a numerical example.