Knowledge graphs (KGs) are of great importance in various artificial intelligence systems, such as question answering, relation extraction, and recommendation. Nevertheless, most real-world KGs are highly incomplete, with many missing relations between entities. To discover new triples (i.e., head entity, relation, tail entity), many KG completion algorithms have been proposed in recent years. However, a vast majority of existing studies often require a large number of training triples for each relation, which contradicts the fact that the frequency distribution of relations in KGs often follows a long tail distribution, meaning a majority of relations have only very few triples. Meanwhile, since most existing large-scale KGs are constructed automatically by extracting information from crowd-sourcing data using heuristic algorithms, plenty of errors could be inevitably incorporated due to the lack of human verification, which greatly reduces the performance for KG completion. To tackle the aforementioned issues, in this paper, we study a novel problem of error-aware few-shot KG completion and present a principled KG completion framework REFORM. Specifically, we formulate the problem under the few-shot learning framework, and our goal is to accumulate meta-knowledge across different meta-tasks and generalize the accumulated knowledge to the meta-test task for error-aware few-shot KG completion. To address the associated challenges resulting from insufficient training samples and inevitable errors, we propose three essential modules neighbor encoder, cross-relation aggregation, and error mitigation in each meta-task. Extensive experiments on three widely used KG datasets demonstrate the superiority of the proposed framework REFORM over competitive baseline methods.