Millions of people are suffering from cancers, but accurate early diagnosis and effective treatment are still tough for all doctors. In recent years, long non-coding RNAs (lncRNAs) have been proven to play an important role in diseases, especially cancers. These lncRNAs execute their functions by regulating gene expression. Therefore, identifying lncRNAs which are related to cancers could help researchers gain a deeper understanding of cancer mechanisms and help them find treatment options. A large number of relationships between lncRNAs and cancers have been verified by biological experiments, which give us a chance to use computational methods to identify cancer-related lncRNAs. In this paper, we applied the convolutional neural network (CNN) to identify cancer-related lncRNAs by lncRNA's target genes and their tissue expression specificity. Since lncRNA regulates target gene expression and it has been reported to have tissue expression specificity, their target genes and expression in different tissues were used as features of lncRNAs. Then, the deep belief network (DBN) was used to unsupervised encode features of lncRNAs. Finally, CNN was used to predict cancer-related lncRNAs based on known relationships between lncRNAs and cancers. For each type of cancer, we built a CNN model to predict its related lncRNAs. We identified more related lncRNAs for 41 kinds of cancers. Ten-cross validation has been used to prove the performance of our method. The results showed that our method is better than several previous methods with area under the curve (AUC) 0.81 and area under the precision-recall curve (AUPR) 0.79. To verify the accuracy of our results, case studies have been done.