Knowledge graphs have powerful reasoning capabilities, but they suffer from incompleteness and long-tail distributions of relations. Few-shot knowledge graph (KG) completion aims to address these issues by completing missing triplets for few-shot relations which only have limited existing triplets. Existing methods attempt to learn few-shot relation embeddings by utilizing the head and tail entity embeddings within the same triplets. Such entity embeddings are enhanced from their respective neighborhoods, but these methods fail to select crucial neighbor entities relevant to the relations. In this paper, to solve this problem, we propose a new Supervised Relational Learning (SuperRL) model with selective neighbor entities for few-shot KG completion. In SuperRL, we first enhance head and tail entity embeddings based on a cascaded embedding enhancement network with different neighbor entity encoders, which can select crucial neighbor entities for few-shot relations from different perspectives. We then jointly perform dual contrastive learning and metric learning to provide different supervision signals for relational learning. Extensive experiments on benchmark datasets have substantiated the superiority of SuperRL in different evaluation metrics over the state-of-the art baselines. The source code is publicly available at: https://github.com/seucoin/SuperRL .