Human activity prediction has become a prerequisite foundation for service recommendation and anomaly detection systems in a smart space filled with various Internet of things (IoT). In this paper, we present a novel approach to predict the next activity in a multi-user smart space. While the majority of previous studies focused on single-user activities, our study considers multi-user activities that occur with a large variety of patterns. We determined the attributes of a multi-user environment and utilized them for the prediction performance. In a multi-user smart space, there exist multiple next activities after a sequence of activities occurs. Moreover, activities often occur concurrently with a group of people who have a common intention together, e.g., a presentation. In order to solve the multiple next-activity existence problem, we propose the next-activity set prediction rather than activity prediction. We also propose sequence partitioning to reduce the complexity of activity patterns. Relatively more activities occur at the beginning and end of an activity sequence. Using these characteristics, we suggest dividing the activity sequences into two states when the time interval between two activities is longer than a time threshold value. Subsequently, the next-activity set is predicted by utilizing a long short-term memory model for each state. To evaluate the proposed approach, we experimented using not only a real dataset generated from our campus testbed but also a single-user dataset. Our experiments showed high accuracy of next-activity set prediction in both environments. Thus, the results confirmed that our proposed method can be effectively utilized for various context-aware applications in a smart space.