Self-localization and tracking a moving object is a key technology for service robot interactive applications. Most tracking algorithms focus on how to correctly estimate the acceleration, velocity, and position of the moving objects based on the prior states and sensor information. What has not been studied so far is tracking the partially observable moving object which is often hidden from a robot's view using lasers. Applying the traditional tracking algorithms will lead to the divergent estimation of the object's position. Therefore, in this paper, we propose a novel laser based partially observable moving object tracking and self-localization algorithm. We adopt stream functions and Rao-Blackwellised particle filter (RBPF) to predict where the partially observable moving object will go in previously mapped environmental features. Moreover, a robot can localize itself and track such a moving object according to stream field. Our experimental results show the proposed algorithm can localize itself and track the partially observable moving object effectively.