Recognizing human activity is one of the important areas of computer vision research today. It plays a vital role in constructing intelligent surveillance systems. Despite the efforts in the past decades, recognizing human activities from videos is still a challenging task. Human activity may have different forms ranging from simple actions to complex activities. Recently released depth cameras provide effective estimation of 3D positions of skeletal joints in temporal sequences of depth maps. In this paper, a system for human activity recognition is proposed. We have considered the task of obtaining a descriptive labeling of the activities being performed through labeling human sub-activities. The activities we consider happen over a long period, and comprise several sub-activities performed in a sequence. The proposed activity descriptor makes the activity recognition problem viewed as a sequence classification problem. The proposed system employs Hidden Markov Models (HMMs) to recognize human activities. The system is evaluated on two benchmark datasets for daily living activity recognition. Experiment results demonstrate that the proposed system outperforms the state-of-the-art methods.