This paper presents an application of the Markov Decision Processes to search a target with a mobile robot. The robot does not know the absolute position of the target. It only knows the position of the target relative to its position. Markov Decision Processes have been widely used in mobile robotics. In this paper, we show experimentally that they are well suited for our task. Moreover, we explain how the mobile robot plans and re-plans a path to the target taking into account the incomplete knowledge it has on the target. Some simulation experiments are given.