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Background Long-chain non-coding RNA (lncRNA) is closely related to many biological activities. Since its sequence structure is similar to that of messenger RNA (mRNA), it is difficult to distinguish between the two based only on sequence biometrics. Therefore, it is particularly important to construct a model that can effectively identify lncRNA and mRNA. Results First, the difference in the k-mer frequency distribution between lncRNA and mRNA sequences is considered in this paper, and they are transformed into the k-mer frequency matrix. Moreover, k-mers with more species are screened by relative entropy. The classification model of the lncRNA and mRNA sequences is then proposed by inputting the k-mer frequency matrix and training the convolutional neural network. Finally, the optimal k-mer combination of the classification model is determined and compared with other machine learning methods in humans, mice and chickens. The results indicate that the proposed model has the highest classification accuracy. Furthermore, the recognition ability of this model is verified to a single sequence. Conclusion We established a classification model for lncRNA and mRNA based on k-mers and the convolutional neural network. The classification accuracy of the model with 1-mers, 2-mers and 3-mers was the highest, with an accuracy of 0.9872 in humans, 0.8797 in mice and 0.9963 in chickens, which is better than those of the random forest, logistic regression, decision tree and support vector machine.