We show that a suitable combination of flat-band ferromagnetism,geometry and nontrivial electronic band topol-ogy can give rise to itinerant topological magnons.An SU(2) symmetric topological Hubbard model with nearly flat electronic bands,on a Kagome lattice,is considered as the prototype.This model exhibits ferromagnetic order when the lowest electronic band is half-filled.Using the numerical exact diagonalization method with a projection onto this nearly flat band,we can obtain the magnonic spectra.In the flat-band limit,the spectra exhibit distinct dispersions with Dirac points,similar to those of free electrons with isotropic hoppings,or a local spin magnet with pure ferromagnetic Heisenberg exchanges on the same geometry.Significantly,the non-flatness of the electronic band may induce a topological gap at the Dirac points,leading to a magnonic band with a nonzero Chern number.More intriguingly,this magnonic Chern number changes its sign when the topological index of the electronic band is reversed,suggesting that the nontrivial topology of the magnonic band is related to its underlying electronic band.Our work suggests interesting directions for the further exploration of,and searches for,itinerant topological magnons.