Graph classification is a highly impactful task that plays a crucial role in a myriad of real-world applications such as molecular property prediction and protein function prediction. Aiming to handle the new classes with limited labeled graphs, few-shot graph classification has become a bridge of existing graph classification solutions and practical usage. This work explores the potential of metric-based meta-learning for solving few-shot graph classification. We highlight the importance of considering structural characteristics in the solution and propose a novel framework which explicitly considers global structure and local structure of the input graph. An implementation upon GIN, named SMFGIN, is tested on two datasets, Chembl and TRIANGLES, where extensive experiments validate the effectiveness of the proposed method. The Chembl is constructed to fill in the gap of lacking largescale benchmark for few-shot graph classification evaluation, which will be released together with the implementation of SMF-GIN upon acceptance