Cascade transition between energy levels has important applications, such as in quantum information protocols and quantum cascade lasers. In two-dimensional heterostructure, the moir\'e superlattice potential can result in multiple interlayer exciton (IX) energy levels. We demonstrate the cascade transitions between such moir\'e IXs by performing time- and energy-resolved photoluminescence measurements. We show that the lower-energy moir\'e IX can be excited to higher-energy ones, facilitating IX population inversion.