The Madden-Julian Oscillation (MJO) intensity and propagation undergo significant year-to-year variations, behind which the leading mode of the tropical 2-7-year variability (e.g., El Niño-Southern Oscillation, ENSO) plays an important role. Despite many studies focused on the impacts of the diversified ENSO warm phases on MJO, no one has ever tried to understand the possible MJO variations in different types of ENSO cold phases (i.e., La Niña). Here, we find that MJO tends to be broader, stronger and faster when a La Niña has its cooling center over the eastern Pacific. However, when the La Niña cooling peaks over the central Pacific, the atmosphere ahead of MJO becomes drier and more stabilized, and thus the MJO eastward propagation is constrained, slower and weaker. The remote influences of MJO over North America (East Asia) are likely stronger when the La Niña cooling center shifts eastward (westward). These results help us construct a whole paradigm of ENSO diversity influencing MJO and also support the necessity to consider the two types of La Niña when exploring different ENSO impacts on global weather and climate.