Edge computing, which provides computation services at the edge of networks, has become a promising method to meet the massive computation demands of Internet of Things (IoT). To make full use of resources, a computation offloading scheme is needed in edge computing system. In this work, we propose an event-driven computation offloading scheme for the first time. Compared with the existing time-driven schemes, the proposed scheme has a smaller implementation complexity in some scenarios with computation-intensive task computing. In the proposed scheme, the priority of different tasks is jointly considered. To decide the optimal offloading action of the scheme, we formulate the offloading problem as a semi-Markov decision process (SMDP). Then, a model-based method is proposed to derive the optimal offloading policy under fully explored system by addressing the challengs of modeling. On the other hand, considering partially explored system, we propose an online double deep Q-network algorithm, which can deal with the poor scalability of the standard Q-learning algorithm, to derive the optimal offloading policy. In addition, we also introduce some tricks to accelerate the learning procedure. The simulation results show the superior performance of our proposed scheme.