Recent studies uncover a diversity in the Madden-Julian Oscillation (MJO) propagation in the observations. Four types of MJO events including stand, jump, slow, and fast MJO are identified. We apply the same classification algorithm to a set of Energy Exascale Earth System Model version 2 (E3SMv2) simulation with 5 ensemble members. Results show that E3SMv2 also captures the four types of MJO as seen in the observations. However, the portion of the stand and jump MJO events in E3SMv2 is much higher than that in the observation, indicating an exaggerated barrier effect of the Maritime Continent on MJO propagation in the model. The jump MJO in E3SMv2 is also biased with a westward propagation for the simulated convection over the Indian Ocean, which is opposite to its eastward propagation in the observations. For all four types of MJO, the simulated shallower MJO convection and its weaker westward-tilted structure are reasons for their biased propagation in the model. The drift of the seasonal mean moist static energy is also responsible for the MJO diversity biases in E3SMv2. These biases in the simulated MJO diversity lead to distinct differences in the MJO teleconnections at middle latitudes between the model and the observations, which is fundamental to the skillful subseasonal to seasonal weather predictions.