In this paper, we examine the problem of designing parameter-dependent H-infinity filters for output estimation in an LPV plant that includes a constant state delay. The state-space data are assumed to depend on parameters that are measurable in real-time. We develop linear matrix inequality (LMI) based delay-dependent conditions to guarantee both asymptotic stability and L-2 gain performance, and we provide an explicit solution for the filters' state-space matrices in terms of LMIs. By taking the estimation error into account in the H-infinity criterion, the designed filters have the capability of tracking the outputs of the plant in the presence of external disturbances. Our technique reduces to delay-independent analysis conditions by relaxing some of the LMI decision variables, and results of previous works are shown to be particular cases of the present work. We examine both memoryless and state delayed filters that include delay terms to reduce conservatism in the design. Illustrative examples are used to demonstrate the proposed methodology for filter design and show the superiority of using the proposed delayed configuration for the H-infinity filters compared to the memoryless filters.