Functional connectivity (FC) analysis, which measures the connection between different brain regions, has been widely used to study brain function and development. However, FC-based analysis breaks the local structure in MRI images, resulting in a challenge for applying advanced deep learning models, e.g., convolutional neural networks (CNN). To fit the data in a non-Euclidean domain, graph convolutional neural network (GCN) was proposed, which can work on graphs rather than raw images, making it a suitable model for brain FC study. The small sample size is another challenge. Compared with natural images, medical images are usually limited in data sample size. Moreover, labeling medical images requires laborious annotation and is time-consuming. These limitations result in low accuracy and overfitting problem when training a conventional deep learning model on medical images. To address this problem, we employed a semi-supervised GCN with a Laplacian regularization term. By exploiting the between-sample information, semi-supervised GCN can achieve better performance on data with limited sample size. We applied the semi-supervised GCN model to a brain imaging cohort to classify the groups with different Wide Range Achievement Test (WRAT) scores. Experimental results showed semi-supervised GCN can improve classification accuracy, demonstrating the superior power of semi-supervised GCN on small datasets.