In　this　note,　a　robust　finite-horizon　Kalman　filter　is　designed　for　discrete　time-varying　uncertain　systems　with　both　additive　and　multiplicative　noises.　The　system　under　consideration　is　subject　to　both　deterministic　and　stochastic　uncertainties.　Sufficient　conditions　for　the　filter　to　guarantee　an　optimized　upper　bound　on　the　state　estimation　error　variance　for　admissible　uncertainties　are　established　in　terms　of　two　discrete　Riccati　difference　equations.　A　numerical　example　is　given　to　show　the　applicability　of　the　presented　method.