We study the magnon bands of twisted bilayer honeycomb quantum magnets using linear spin wave the-ory.Although the interlayer coupling can be ferromagnetic or antiferromagnetic,we keep the intralayer one ferromagnetic to avoid possible frustration.For the interlayer ferromagnetic case,we find the magnon bands have similar features with the corresponding electronic energy spectrums.Although the linear dispersions near the Dirac points are preserved in the magnon bands of twisted bilayer magnets,their slopes are reduced with the decrease of the twist angles.On the other hand,the interlayer antiferromagnetic couplings generate quite different magnon spectra.The two single-layered magnon spectra are usually decoupled due to the opposite orientations of the spins in the two layers.We also develop a low-energy continuous theory for very small twist angles,which has been verified to fit well with the exact tight-binding calculations.Our results may be experimentally observed due to the rapid progress in two-dimensional magnetic materials.