CircRNA is a new type of non-coding RNA with a closed loop structure. More and more biological experiments show that circRNA plays important roles in many diseases by regulating the target genes of miRNA. Therefore, correct identification of the potential interaction between circRNA and miRNA not only helps to understand the mechanism of the disease, but also contributes to the diagnosis, treatment, and prognosis of the disease. In this study, we propose a model (IIMCCMA) by using network embedding and matrix completion to predict the potential interaction of circRNA-miRNA. Firstly, the corresponding adjacency matrix is constructed based on the experimentally verified circRNA-miRNA interaction, circRNA-cancer interaction, and miRNA-cancer interaction. Then, the Gaussian kernel function and the cosine function are used to calculate the circRNA Gaussian interaction profile kernel similarity, circRNA functional similarity, miRNA Gaussian interaction profile kernel similarity, and miRNA functional similarity. In order to reduce the influence of noise and redundant information in known interactions, this model uses network embedding to extract the potential feature vectors of circRNA and miRNA, respectively. Finally, an improved inductive matrix completion algorithm based on the feature vectors of circRNA and miRNA is used to identify potential interactions between circRNAs and miRNAs. The 10-fold cross-validation experiment is utilized to prove the predictive ability of the IIMCCMA. The experimental results show that the AUC value and AUPR value of the IIMCCMA model are higher than other state-of-the-art algorithms. In addition, case studies show that the IIMCCMA model can correctly identify the potential interactions between circRNAs and miRNAs.