Numerous studies show that circular RNA (circRNA) functions as a sponge for microRNA (miRNA), significantly regulating gene expression by interacting with miRNA, which in turn affects the progression of human diseases. Traditional experimental approaches for investigating circRNA-miRNA interactions (CMI) are both time-consuming and costly, making computational methods a valuable alternative. Hence, we propose a computational model for predicting CMI, leveraging a ybrid multmodal nework and igher-order nighborhood infomation (Hither-CMI). Specifically, Hither-CMI employs Multiple Kernel Learning (MKL) to integrate sequence, structure, and expression similarity networks of circRNA and miRNA, resulting in a hybrid multimodal network. Next, an enhanced Graph Convolutional Network (GCN) is utilized to combine the circRNA-miRNA hybrid multimodal network with the CMI association network, producing a hybrid higher-order embedding representation. Finally, the XGBoost classifier is applied for training and prediction. The Hither-CMI model achieved a predicted AUC value of 0.9134. In case studies, 25 out of the top 30 predicted CMI were confirmed by recent literature. These extensive experimental results further validate the effectiveness of Hither-CMI in predicting potential CMI, making it a promising prescreening tool for further biological research.