Graph data is ubiquitous in real-world applications, and graph neural networks (GNNs) have been widely used in graph data analysis. However, the performance of GNNs can be severely impacted by adversarial attacks on graph structures. Existing defense methods against adversarial attacks generally rely on low-rank graph structure reconstruction based on graph community preservation priors. However, existing graph structure adversarial defense methods cannot adaptively seek the true low-rank value for graph structure reconstruction, and low-rank graph structures are semantically mismatched with downstream tasks. To address these problems, this study proposes the over-parameterized graph neural network (OPGNN) method based on the implicit regularization effect of over-parameterization. In addition, it formally proves that this method can adaptively solve the low-rank graph structure problem and also proves that over-parameterized residual links on node deep representations can effectively address semantic mismatch. Experimental results on real datasets demonstrate that the OPGNN method is more robust than existing baseline methods, and the OPGNN framework is notably effective on different graph neural network backbones such as GCN, APPNP, and GPRGNN.