Abstract Recent studies have shown that individual Madden–Julian oscillation (MJO) events can be categorized into four types based on their propagation characteristics: standing, jumping, slow-propagating, and fast-propagating MJOs. While their structures and impacts are well documented in observations, their representation in state-of-the-art climate models has not been investigated. This study evaluates the four types of MJOs in phase 6 of Coupled Model Intercomparison Project (CMIP6) models. While most models show reasonable MJO propagation characteristics, their performance varies among MJO types, with better performance for the propagating MJO types. To identify the factors that drive each MJO type, background conditions at the surface, troposphere, and stratosphere are examined. We found that the standing and fast MJOs are closely associated with sea surface temperature (SST) and precipitable water (PW) distributions. Specifically, negative and positive SST and PW anomalies are observed over the equatorial Pacific during the standing and fast-propagating MJOs, respectively. In contrast, the jumping and slow-propagating MJOs do not show noticeable SST and PW distributions, suggesting that they may be more strongly influenced by the internal dynamics than by the background conditions. It is further found that the models with more frequent standing MJO than fast MJO generally have stronger negative biases in both SST and PW over the equatorial western Pacific. Although the standing MJO is also preferred when the stratospheric wind at 50 hPa is westerly, such a relationship is absent in the models. These results suggest that MJO diversity in climate models could be improved by better simulation of the mean state, especially for the standing and fast-propagating MJOs.