Process mining aims at distilling useful knowledge from the execution logs of process models. It has become a vivid research area in recent years. In this paper, a novel approach for process mining based on two event types, i.e., START and COMPLETE, is proposed. Information about the start and completion of tasks can be used to explicitly detect parallelism. The algorithm presented in this paper overcomes some of the limitations of existing algorithms such as the ?-algorithm (e.g., short-loops) and therefore enhances the applicability of process mining in practical situations. Based on the completeness of the given event log and the behavior theory of Petri nets, the correctness of the algorithm can be proved theoretically.