In this work, we estimate the synchrotron radiation of cosmic muons in a uniform magnetic field in the μeV-to-meV energy scale. Such events can potentially bring backgrounds to the axion dark matter searches. GEANT4 software package is utilized to simulate the muon tracks in a cylindrical region of interest with 8 T solenoid magnetic field applied. We further develop analytical estimation of the angular-frequency-differential synchrotron radiation power spectra for this work since the cosmic muons spread a wide range of Lorentz factor γ and pitch angle α. We verify that the natural charged particles are not the dominant noise backgrounds for the current axion dark matter experiments on the μeV scale because of the high quality factor Q and fine energy resolution in the readout. However, without sufficient energy resolution in the detector readout, future broadband axion dark matter experiments might be vulnerable to the synchrotron radiation of these charged particles.