With the increasing demands of training graph neural networks (GNNs) on large-scale graphs, graph data condensation has emerged as a critical technique to relieve the storage and time costs during the training phase. It aims to condense the original large-scale graph to a much smaller synthetic graph while preserving the essential information necessary for efficiently training a downstream GNN. However, existing methods concentrate either on optimizing node features exclusively or endeavor to independently learn node features and the graph structure generator. They could not explicitly leverage the information of the original graph structure and failed to construct an interpretable graph structure for the synthetic dataset. To address these issues, we introduce a novel framework named Graph Data Condensation via Self-expressive Graph Structure Reconstruction (GCSR). Our method stands out by (1) explicitly incorporating the original graph structure into the condensing process and (2) capturing the nuanced interdependencies between the condensed nodes by reconstructing an interpretable self-expressive graph structure. Extensive experiments and comprehensive analysis validate the efficacy of the proposed method across diverse GNN models and datasets. Our code is available at https://github.com/zclzcl0223/GCSR.