The concept of a smart home has been discussed in recent years. Its primary purpose is to make life more convenient, safe, and fun in various areas, including home automation, security, entertainment, and so on. In order to automate the interactions between the inhabitants and devices in a home, the prediction of the inhabitant’s actions is very important. Current prediction algorithms are usually based on the order of actions to be taken. However, the prediction accuracy of those algorithms is not satisfactory. This is because actions can be separated into a set of groups, and actions in the same group are usually taken in an almost arbitrary order. The set of groups should be discovered before the prediction of actions. In this paper, an action group discovery (AGD) algorithm is proposed. The AGD algorithm is based on the 1-order Markov model and a reverse 1-order Markov model. According to the combination of the two models, a set of group pairs is generated. Then, the action groups are generated by merging these group pairs. A group discovery rate (GDRate) is defined to evaluate the efficiency of the AGD algorithm. Experimental results show that the AGD algorithm can discover most action groups in various situations. The AGD algorithm is thus helpful for predicting actions.