This paper is concerned with the reduced-order H∞ filtering problem for Markovian jump systems with time delays, which are time-varying and depend on the system mode. Sufficient conditions for the existence of the reduced-order H∞ filtering are provided in terms of linear matrix inequalities (LMIs) with equality constraints. It is shown that the conditions for the existence of zeroth-order H∞ filtering can be expressed by LMIs without any equality constraints. A globally convergent algorithm involving LMIs based on the sequential linear programming matrix is suggested to solve the matrix inequalities characterizing the filtering solutions. Using the numerical solutions of the matrix inequalities, a reduced-order filtering with error less than some prescribed scalar can be computed. Finally, an illustrative example is presented to show the effectiveness of the proposed approach. ©2008ElsevierB.V.Allrightsreserved.