Monitoring human physical activity has become an important research area and is essential to evaluate the degree of functional performance and general level of activity of a person. The discrimination of daily living activities can be implemented with machine learning techniques. A public dataset provided during the European Symposium on Artificial Neural Networks 2013, with time and frequency domain features extracted from raw signals of the smartphone inertial sensors, was used to implement and evaluate an activity classifier. Using a decision tree classifier, an accuracy of 86% was achieved for the classification of walk, climb stairs, stand, sit, and lay down. The results obtained suggest that the smartphone's inertial sensors could be used for an accurate physical activity classification even with real-time requirements.