Graph classification aims to extract accurate information from graph-structured data for classification and is becoming more and more important in graph learning community. Although Graph Neural Networks (GNNs) have been successfully applied to graph classification tasks, most of them overlook the scarcity of labeled graph data in many applications. For example, in bioinformatics, obtaining protein graph labels usually needs laborious experiments. Recently, few-shot learning has been explored to alleviate this problem with only given a few labeled graph samples of test classes. The shared sub-structures between training classes and test classes are essential in few-shot graph classification. Exiting methods assume that the test classes belong to the same set of super-classes clustered from training classes. However, according to our observations, the label spaces of training classes and test classes usually do not overlap in real-world scenario. As a result, the existing methods don't well capture the local structures of unseen test classes. To overcome the limitation, in this paper, we propose a direct method to capture the sub-structures with well initialized meta-learner within a few adaptation steps. More specifically, (1) we propose a novel framework consisting of a graph meta-learner, which uses GNNs based modules for fast adaptation on graph data, and a step controller for the robustness and generalization of meta-learner; (2) we provide quantitative analysis for the framework and give a graph-dependent upper bound of the generalization error based on our framework; (3) the extensive experiments on real-world datasets demonstrate that our framework gets state-of-the-art results on several few-shot graph classification tasks compared to baselines.