Summary: This paper investigates the robust guaranteed cost observer design for a class of linear descriptor systems with state delays and Markovian jumping parameters. The system under study involves time delays, jumping parameters and uncertainties. The transition of the jumping parameters in systems is governed by a finite-state Markov process. The objective is to design linear memoryless observers such that for all uncertainties the resulting augmented system is regular, impulse free, robust stochastically stable independent of delays and satisfies the proposed guaranteed cost performance. Based on stability theory in stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost observers is derived. Robust guaranteed cost filters are designed in terms of linear matrix inequalities (LMIs). A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost observer.