MicroRNAs (miRNAs) play a critical role in human diseases. Determining the association between miRNAs and disease contributes to elucidating the pathogenesis of liver diseases and seeking the effective treatment method. Despite great recent advances in the field of the associations between miRNAs and diseases, implementing association verification and recognition efficiently at scale presents serious challenges to biological experimental approaches. Thus, computational methods for predicting miRNA-disease association have become a research hotspot. In this paper, we present a new computational method, named distance-based sequence similarity for miRNA-disease association prediction (DBMDA), that directly learns a mapping from miRNA sequence to a Euclidean space. The notable feature of our approach consists of inferring global similarity from region distances that can be figured by chaos game representation algorithm based on the miRNA sequences. In the 5-fold cross-validation experiment, the area under the curve (AUC) obtained by DBMDA in predicting potential miRNA-disease associations reached 0.9129. To assess the effectiveness of DBMDA more effectively, we compared it with different classifiers and former prediction models. Besides, we constructed two case studies for prostate neoplasms and colon neoplasms. Results show that 39 and 39 out of the top 40 predicted miRNAs were confirmed by other databases, respectively. BDMDA has made new attempts in sequence similarity and achieved excellent results, while at the same time providing a new perspective for predicting the relationship between diseases and miRNAs. The source code and datasets explored in this work are available online from the University of Chinese Academy of Sciences (http://220.171.34.3:81/).