Over the past few years, graph representation learning (GRL) has received widespread attention on the feature representations of the non-Euclidean data. As a typical model of GRL, graph convolutional networks (GCN) fuse the graph Laplacian-based static sample structural information. GCN thus generalizes convolutional neural networks to acquire the sample representations with the variously high-order structures. However, most of existing GCN-based variants depend on the static data structural relationships. It will result in the extracted data features lacking of representativeness during the convolution process. To solve this problem, dynamic graph learning convolutional networks (DGLCN) on the application of semi-supervised classification are proposed. First, we introduce a definition of dynamic spectral graph convolution operation. It constantly optimizes the high-order structural relationships between data points according to the loss values of the loss function, and then fits the local geometry information of data exactly. After optimizing our proposed definition with the one-order Chebyshev polynomial, we can obtain a single-layer convolution rule of DGLCN. Due to the fusion of the optimized structural information in the learning process, multi-layer DGLCN can extract richer sample features to improve classification performance. Substantial experiments are conducted on citation network datasets to prove the effectiveness of DGLCN. Experiment results demonstrate that the proposed DGLCN obtains a superior classification performance compared to several existing semi-supervised classification models.