This paper introduces a novel approach for real-time classification of human activities using data from inertial sensors embedded in a smartphone. We propose a hierarchical classification scheme to recognize seven classes of activities including postural transitions. Its structure has three internal nodes composed of three Support Vector Machines (SVMs) classifiers, each one is associated with a set of activities. Moreover, each SVMs is fed with a feature vector from an adapted and optimal frequency band. Experimental results conducted on a challenging publicly available dataset named SBHAR show that our method is effective and outperforms various state-of-the-art approaches. We also show the suitability of our method to recognize postural transitions.