This paper shows the infinite horizon model of Partially Observable Markov Decision Process with lagged information. The lagged information is uncertain delayed observation of the process under control. Even though the optimal policy of the model exists, finding the optimal policy is very time consuming. Thus, the aim of this study is to find an .eplison.-optimal stationary policy minimizing the expected discounted total cost of the model. .EPSILON.- optimal policy is found by using a modified version of the well known policy iteration algorithm. The modification focuses to the value determination routine of the algorithm. Some properties of the approximation functions for the expected discounted cost of a stationary policy are presented. The expected discounted cost of a stationary policy is approximated based on these properties. A numerical example is also shown.