Objective N⁶-methyladenosine (m⁶A) is the most common and abundant chemical modification in RNA and plays an important role in many biological processes. Several computational methods have been developed to predict m⁶A methylation sites. However, these methods lack robustness when targeting different species or different tissues. To improve the robustness of the prediction performance of m⁶A methylation sites in different tissues, this paper proposed a double-layer bidirectional gated recurrent unit (BiGRU) network model that combines reverse sequence information to extract higher-level features of the data.Methods Some representative mammalian tissue m⁶A methylation site datasets were selected as the training datasets. Based on a BiGRU, a double-layer BiGRU network was constructed by collocation of the model network, the model structure, the number of layers and the optimizer.Results The model was applied to predict m⁶A methylation sites in 11 human, mouse and rat tissues, and the prediction performance was compared with that of other methods using the same tissues. The results demonstrated that the average area under the receiver operating characteristic curve (AUC) predicted by the proposed model reached 93.72%, equaling that of the best prediction method at present. The values of accuracy (ACC), sensitivity (SN), specificity (SP) and Matthews correlation coefficient (MCC) were 90.07%, 90.30%, 89.84% and 80.17%, respectively, which were higher than those of the current methods for predicting m⁶A methylation sites.Conclusion Compared with that of existing research methods, the prediction accuracy of the double-layer BiGRU network was the highest for identifying m⁶A methylation sites in the 11 tissues, indicating that the method proposed in this study has an excellent generalizability.