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We propose a scheme for realizing high-fidelity topological state transfer via the topological edge states in a one-dimensional cavity-magnon system. We find that the cavity-magnon system can be mapped analytically into the generalized Su-Schrieffer-Heeger model with tunable cavity-magnon coupling. It can be shown that the edge state can be served as a quantum channel to realize the photonic and magnonic state transfers by adjusting the coupling strength between adjacent cavity modes. Further, our scheme can realize the quantum state transfer between photonic state and magnonic state by changing the cavity-magnon coupling strength. With the numerical simulation, we quantitatively show that the photonic, magnonic and magnon-to-photon state transfers can be achieved with high fidelity in the cavity-magnon system. Spectacularly, three different types of quantum state transfer schemes can be even transformed into each other in a controllable fashion. The Su-Schrieffer-Heeger model based on the cavity-magnon system provides us a tunable platform to engineer the transport of photon and magnon, which may have potential applications in topological quantum processing.

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