Link prediction for knowledge graphs aims to predict missing connections between entities. Prevailing methods are limited to a transductive setting and hard to process unseen entities. The recent proposed subgraph-based models provided alternatives to predict links from the subgraph structure surrounding a candidate triplet. However, these methods require abundant known facts of training triplets and perform poorly on relationships that only have a few triplets. In this paper, we propose Meta-iKG, a novel subgraph-based meta-learner for few-shot inductive relation reasoning. Meta-iKG utilizes local subgraphs to transfer subgraph-specific information and learn transferable patterns faster via meta gradients. In this way, we find the model can quickly adapt to few-shot relationships using only a handful of known facts with inductive settings. Moreover, we introduce a large-shot relation update procedure to traditional meta-learning to ensure that our model can generalize well both on few-shot and large-shot relations. We evaluate Meta-iKG on inductive benchmarks sampled from NELL and Freebase, and the results show that Meta-iKG outperforms the current state-of-the-art methods both in few-shot scenarios and standard inductive settings.