Accumulating experimental studies have indicated that lncRNAs play important roles in various critical biological process and their alterations and dysregulations have been associated with many important complex diseases. Developing effective computational models to predict potential disease-lncRNA association could benefit not only the understanding of disease mechanism at lncRNA level, but also the detection of disease biomarkers for disease diagnosis, treatment, prognosis and prevention. However, known experimentally confirmed disease-lncRNA associations are still very limited. In this study, a novel model of HyperGeometric distribution for LncRNA-Disease Association inference (HGLDA) was developed to predict lncRNA-disease associations by integrating miRNA-disease associations and lncRNA-miRNA interactions. Although HGLDA didn't rely on any known disease-lncRNA associations, it still obtained an AUC of 0.7621 in the leave-one-out cross validation. Furthermore, 19 predicted associations for breast cancer, lung cancer, and colorectal cancer were verified by biological experimental studies. Furthermore, the model of LncRNA Functional Similarity Calculation based on the information of MiRNA (LFSCM) was developed to calculate lncRNA functional similarity on a large scale by integrating disease semantic similarity, miRNA-disease associations, and miRNA-lncRNA interactions. It is anticipated that HGLDA and LFSCM could be effective biological tools for biomedical research.