Consider a scenario in which a smart phone automatically saves the user’s positional records for personalized location-based applications. The smart phone will infer patterns of user activities from the historical records and predict user’s future movements. In this paper, we present algorithms for mining the evolving positional logs in order to identify places of significance to user and representative paths connecting these places, based on which a personalized user activity map is constructed. In addition, the map is designed to contain information of speed and transition probabilities, which are used in predicting the user’s future movements. Our experiments show that the user activity map well matches the actual traces and works effectively in predicting user’s movements.