The automated learning of action models is widely recognised as a key and compelling challenge to address the difficulties of the manual specification of planning domains. Most state-of-the-art methods perform this learning offline from an input set of plan traces generated by the execution of (successful) plans. However, how to generate informative plan traces for learning action models is still an open issue. Moreover, plan traces might not be available for a new environment. In this paper, we propose an algorithm for learning action models online, incrementally during the execution of plans. Such plans are generated to achieve goals that the algorithm decides online in order to obtain informative plan traces and reach states from which useful information can be learned. We show some fundamental theoretical properties of the algorithm, and we experimentally evaluate the online learning of the action models over a large set of IPC domains.