The cold tongue mode (CTM), which represents the out-of-phase relationship in sea surface temperature anomaly (SSTA) variability between the Pacific cold tongue region and elsewhere in the tropical Pacific, shows a long-term cooling trend in the eastern equatorial Pacific. In this study, we investigate how well the CTM is reproduced in historical simulations generated by the 20 models considered in Phase 5 of the Coupled Model Intercomparison Project (CMIP5). Qualitatively, all 20 models roughly capture the cooling SSTA associated with the CTM. However, a quantitative assessment (i.e., Taylor diagrams and the ratio of the trend between the simulations and observations) shows that only five of these 20 models (i.e., CESM1-CAM5, CMCC-CM, FGOALS-g2, IPSL-CM5B-LR, and NorESM1-M) can reproduce with useful accuracy the spatial pattern and long-term trend of the CTM. We find that these five models generally simulate the main ocean dynamical process associated with the CTM. That is, these models adequately capture the long-term cooling trend in the vertical advection of the anomalous temperature by the mean upwelling. We conclude that the performance of these CMIP5 models, with respect to simulations of the long-term cooling trend associated with the vertical advection, and the related long-term decreasing trend of the vertical gradient of the oceanic temperature anomaly, can play an important role in successful reproduction of the CTM.