Cross-network node classification aims to classify the nodes of unlabeled target network using a labeled source network. Existing methods introduce domain adaptation to address representation discrepancy in closed-set scenario. However, the open-set scenario is widespread in applications, in which, the coexistence and interaction of representation discrepancy and label discrepancy pose a great challenge. To this end, we make the first attempt for cross-network node classification in open-set scenario and propose a novel method based on reconstruction. Firstly, the pseudo unknown class nodes from target network are reconstructed into source network, which addresses label discrepancy by transforming open-set into closed-set with K+1 classes. Secondly, the contrastive-center loss is introduced to enhance the node representations, which aims to identify the unknown nodes from known nodes in networks. And then the invariant representations are learned better to address representation discrepancy. Extensive experiments demonstrate the effectiveness of our method.