Studies have shown that microRNAs are functionally related to human diseases. However, experimental methods for detecting miRNA-disease associations are both time consuming and laborious. Therefore, a large number of computational models for predicting potential miRNA-disease interaction have been proposed. However, few methods take into account the nonlinear structural similarity of miRNAs (diseases) and effectively integrate multiple similar metrics into one network. In this paper, we propose a kernel-based soft-neighborhood network propagation algorithm (LKSNF) to predict potential miRNA-disease interactions, which not only exploits the potential nonlinear relationship, but also effectively integrates different similar measures of miRNA (disease). The results of the 5-fold cross-validation show that the LKSNF model has significantly better predictive performance than other state-of-the-art methods. Case study further illustrates the effectiveness of LKSNF in predicting new miRNA-disease interactions.