Four types of MJO with distinct propagating features including standing, jumping, slow, and fast MJO are represented in the 5-member ensemble historical simulations by the E3SM version 2 (E3SMv2) model. The jumping MJO in the model shows an unrealistic westward propagation over the Indian Ocean. Both slow and fast MJO in E3SMv2 lack continuous eastward propagation over the central-western Pacific compared to the observations. Also, a higher portion of fast MJO is identified in the model simulations along with insufficient slow MJO events. Biases are also found in the vertical structures for the MJO in E3SMv2. The identified MJO convection are universally weaker and shallower. For slow MJO, its convection is less westward-tilted with insufficient leading shallow convection. The significant La Niña-like seasonal mean sea surface temperature (SST) anomalies for standing MJO and the El Niño-like seasonal mean SST anomalies for fast MJO are not captured by E3SMv2. Instead, the slow MJO in the model is accompanied with an El Niño-like seasonal mean SST pattern. The model's capability to correctly simulate each MJO type's mid-latitude teleconnection patterns are also measured. Results show that the teleconnection patterns induced by fast MJO is simulated with the highest skill among the four MJO tyeps in the model, which might be a result of the model's correct simulation of its convective heating evolution with the least biases. The type-by-type diagnostics of the MJO in E3SMv2 help to better understand the simulated MJO as well as its teleconnection bias source in the model.