In recent years, with the development of location-based services and widely-used social networks, people can easily share their activities and location with their friends on the social network. Meanwhile, large amounts of data generated by social networks provide an opportunity for mining user behaviors and realize accurate personalized service recommendations. Previous studies focus on a single Point of Interest (POI) recommendation while few consider recommending a POI sequence. This paper proposes a POI-sequence recommendation method based on an exploitation-exploration strategy. It utilizes the historical data from the social network, fully considers the public preference and user’s personalized preference. After obtaining the exploration score from the historical records, the POI-sequence with the highest overall preference score is recommended to the user. This method can ensure the diversity of recommended POIs. Besides, a breadth-first search method is adopted to improve the recommendation efficiency. Finally, we verify the effectiveness of the proposed method through experiments on real-world datasets.