This study addresses the robust set-membership finite-horizon filtering problem for a class of discrete time-varying systems with missing measurement and polytopic uncertainties in the presence of unknown-but-bounded process and measurement noises. A robust set-membership filter is developed and a recursive algorithm is derived for computing the state estimate ellipsoid that is guaranteed to contain the true state. An optimal possible estimate set is computed recursively by solving the semi-definite programming problem. Simulation results are provided to demonstrate the effectiveness of the proposed method.