Universal domain adaptation (UniDA) aims to transfer knowledge between domains without prior knowledge of the label spaces. Category shift and domain shift are two primary challenges in UniDA, which require the method not only to distinguish common “known” samples from private “unknown” samples but also to align feature distributions of the common samples. In previous works, private samples have been involved to some extent in process of distribution alignment, leading to negative transfer. Therefore, we propose a curriculum adaptation method based on graph neural networks (GNN) to alleviate this issue. Specifically, our paper introduces a score to measure the transferability of samples and a curriculum adaptation strategy which only utilizes the most transferable samples for adaptation in each episode. To prevent classifier from overfitting on source samples, we assist classifier with the score and curriculum learning to obtain reliable pseudo-labels for target common samples. Furthermore, our method utilizes a graph neural network to aggregate features from similar samples across domains. Extensive experiments on three benchmarks demonstrate the effectiveness of our proposed framework.