A map is an abstract internal representation of an environment for a mobile robot, and how to learn it autonomously is one of the most fundamental issues in the research fields of intelligent robotics and artificial intelligence. In this paper, we propose a topological map learning method for mobile robots which constructs a POMDP-based discrete state transition model from time-series data of observations and actions. The main point of this method is to find a set of states or nodes of the map gradually so that it minimizes the three types of entropies or uncertainties of the map about “what observations are obtained”, “what actions are available” and “what state transitions are expected”. It is shown that the topological structure of the state transition model is effectively obtained by this method.