Dysfunction of miRNAs has an important relationship with diseases by impacting their target genes. Identifying disease-related miRNAs is of great significance to prevent and treat diseases. Integrating information of genes related miRNAs and/or diseases in calculational methods for miRNA-disease association studies is meaningful because of the complexity of biological mechanisms. Therefore, in this study, we propose a novel method based on tensor decomposition, termed TDMDA, to integrate multi-type data for identifying pathogenic miRNAs. First, we construct a three-order association tensor to express the associations of miRNA-disease pairs, the associations of miRNA-gene pairs, and the associations of gene-disease pairs simultaneously. Then, a tensor decomposition-based method with auxiliary information is applied to reconstruct the association tensor for predicting miRNA-disease associations, and the auxiliary information includes biological similarity information and adjacency information. The performance of TDMDA is compared with other advanced methods under 5-fold cross-validations. The experimental results indicate the TDMDA is a competitive method.