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While being electrically insulating, magnetic insulators can behave as good spin conductors by carrying spin current with excited spin waves. So far, magnetic insulators are utilized in multilayer heterostructures for optimizing spin transport or to form magnon spin valves for reaching controls over the spin flow. In these studies, it remains an intensively visited topic as to what the corresponding roles of coherent and incoherent magnons are in the spin transmission. Meanwhile, understanding the underlying mechanism associated with spin transmission in insulators can help to identify new mechanisms that can further improve the spin transport efficiency. Here, by studying spin transport in a magnetic‐metal/magnetic‐insulator/platinum multilayer, it is demonstrated that coherent magnons can transfer spins efficiently above the magnon bandgap of magnetic insulators. Particularly the standing spin‐wave mode can greatly enhance the spin flow by inducing a resonant magnon transmission. Furthermore, within the magnon bandgap, a shutdown of spin transmission due to the blocking of coherent magnons is observed. The demonstrated magnon transmission enhancement and filtering effect provides an efficient method for modulating spin current in magnonic devices.