Knowledge base completion (KBC) aims to predict missing information in a knowledge base. In this paper, we address the out-of-knowledge-base (OOKB) entity problem in KBC: how to answer queries concerning test entities not observed at training time. Existing embedding-based KBC models assume that all test entities are available at training time, making it unclear how to obtain embeddings for new entities without costly retraining. To solve the OOKB entity problem without retraining, we use graph neural networks (Graph-NNs) to compute the embeddings of OOKB entities, exploiting the limited auxiliary knowledge provided at test time. The experimental results show the effectiveness of our proposed model in the OOKB setting. Additionally, in the standard KBC setting in which OOKB entities are not involved, our model achieves state-of-the-art performance on the WordNet dataset.