Few-shot Relational Triple Extraction (RTE) aims at detecting emerging relation types along with their entity pairs from unstructured text with the support of a few labeled samples. Prior arts use conditional random field or nearest-neighbor matching strategy to extract entities and use prototypical networks for extracting relations from sentences. Nevertheless, they fail to utilize the triple-level information to verify the plausibility of extracted relational triples, and ignore the proper transfer among the perspectives of entity, relation and triple. To fill in these gaps, in this work, we put forward a novel perspective transfer network (PTN) to address few-shot RTE. Specifically, PTN starts from the relation perspective by checking the existence of a given relation. Then, it transfers to the entity perspective to locate entity spans with relation-specific support sets. Next, it transfers to the triple perspective to validate the plausibility of extracted relational triples. Finally, it transfers back to the relation perspective to check the next relation, and repeats the aforementioned procedure. By transferring among the perspectives of relation, entity, and triple, PTN not only validates the extracted elements at both local and global levels, but also effectively handles more realistic and difficult few-shot RTE scenarios such as multiple triple extraction and nonexistence of triples. Extensive experimental results on existing dataset and new datasets demonstrate that our approach can significantly improve performance over the state-of-the-arts.