Found in recent research, tumor cell invasion, proliferation, or other biological processes are controlled by circular RNA. Understanding the association between circRNAs and diseases is an important way to explore the pathogenesis of complex diseases and promote disease-targeted therapy. Most methods, such as k-mer and PSSM, based on the analysis of high-throughput expression data have the tendency to think functionally similar nucleic acid lack direct linear homology regardless of positional information and only quantify nonlinear sequence relationships. However, in many complex diseases, the sequence nonlinear relationship between the pathogenic nucleic acid and ordinary nucleic acid is not much different. Therefore, the analysis of positional information expression can help to predict the complex associations between circRNA and disease. To fill up this gap, we propose a new method, named iCDA-CGR, to predict the circRNA-disease associations. In particular, we introduce circRNA sequence information and quantifies the sequence nonlinear relationship of circRNA by Chaos Game Representation (CGR) technology based on the biological sequence position information for the first time in the circRNA-disease prediction model. In the cross-validation experiment, our method achieved 0.8533 AUC, which was significantly higher than other existing methods. In the validation of independent data sets including circ2Disease, circRNADisease and CRDD, the prediction accuracy of iCDA-CGR reached 95.18%, 90.64% and 95.89%. Moreover, in the case studies, 19 of the top 30 circRNA-disease associations predicted by iCDA-CGR on circRDisease dataset were confirmed by newly published literature. These results demonstrated that iCDA-CGR has outstanding robustness and stability, and can provide highly credible candidates for biological experiments.