To mitigate the suboptimal nature of graph structure, Graph Structure Learning (GSL) has emerged as a promising approach to improve graph structure and boost performance in downstream tasks. Despite the proposal of numerous GSL methods, the progresses in this field mostly concentrated on node-level tasks, while graph-level tasks (e.g., graph classification) remain largely unexplored. Notably, applying node-level GSL to graph classification is non-trivial due to the lack of find-grained guidance for intricate structure learning. Inspired by the vital role of subgraph in graph classification, in this paper we explore the potential of subgraph structure learning for graph classification by tackling the challenges of key subgraph selection and structure optimization. We propose a novel Motif-driven Subgraph Structure Learning method for Graph Classification (MOSGSL). Specifically, MOSGSL incorporates a subgraph structure learning module which can adaptively select important subgraphs. A motif-driven structure guidance module is further introduced to capture key subgraph-level structural patterns (motifs) and facilitate personalized structure learning. Extensive experiments demonstrate a significant and consistent improvement over baselines, as well as its flexibility and generalizability for various backbones and learning procedures.