We investigate invisible decays of the third neutrino mass eigenstate in future accelerator neutrino experiments using muon-decay beams such as MuOn-decay MEdium baseline NeuTrino beam experiment (MOMENT). MOMENT has outstanding potential to measure the deficit or excess in the spectra caused by neutrino decays, especially in muon neutrino/antineutrino disappearance channels. Such an experiment will improve the constraints of the neutrino lifetime. Compared with exclusion limits in the current accelerator neutrino experiments T2K and NOvA under the stable neutrino assumption, we expect that MOMENT gives the better bound. The non-decay scenario is expected to be excluded by MOMENT at a confidence level of more than 3 $\sigma$, if the best fit results in T2K and NOvA are confirmed. We further find that reducing systematic uncertainties is more important than the running time. Finally, we find some impact of neutrino invisible decays on the precision measurement of other oscillation parameters.