Recent RNA knockdown experiments revealed that a dozen divergent long noncoding RNAs (lncRNAs) positively regulate the transcription of genes in cis. Here, to understand the regulatory mechanism of divergent lncRNAs, we proposed a computational model IRDL (Identify the Regulatory Divergent LncRNAs) to associate divergent lncRNAs with target genes. IRDL took advantage of the cross-tissue paired expression and chromatin accessibility data in ENCODE and a dozen experimentally validated divergent lncRNA target genes. IRDL integrated sequence similarity, co-expression and co-accessibility features, battled the scarcity of gold standard datasets with an increasingly learning framework and identified 446 and 977 divergent lncRNA-gene regulatory associations for mouse and human, respectively. We found that the identified divergent lncRNAs and target genes correlated well in expression and chromatin accessibility. The functional and pathway enrichment analysis suggests that divergent lncRNAs are strongly associated with developmental regulatory transcription factors. The predicted loop structure validation and canonical database search indicate a scaffold regulatory model for divergent lncRNAs. Furthermore, we computationally revealed the tissue/cell-specific regulatory associations considering the specificity of lncRNA. In conclusion, IRDL provides a way to understand the regulatory mechanism of divergent lncRNAs and hints at hundreds of tissue/cell-specific regulatory associations worthy for further biological validation.