Activity prediction aims to predict what activities will occur in the future. In smart homes, to facilitate the daily living of the residents, automated or assistive services are provided. To provide these services, the ability of activity prediction is necessary. When we make a prediction, most of the existing works focus on predicting information about the next activity. However, in a smart home environment, compared with just predicting information about the next activity, another type of activity prediction problem has more practical value: predicting what activities will occur in the coming time period of a certain length. The necessity of this type of prediction is due to the purpose of the smart homes and the character of the activities. Many activities in smart homes need preparation time before being performed. Through this type of prediction, activities could be predicted sufficient time before being performed, and there will be adequate time for the smart home system to prepare corresponding automated or assistive services. As more than one activity could occur within the time period in which the prediction is made, this problem is a multilabel classification problem. In this article, we first give a formulation of the problem. Then, we propose a deep learning model to address it. The proposed model consists of the convolutional part, the long short-term memory layer, and the multilabel output layer. Experiments on real-world datasets show the effectiveness of our model.