  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 an
outstanding performance to measure the deficit or excess in the spectra caused
by neutrino decays, especially in $\nu_\mu$ and $\bar{\nu}_\mu$ disappearance
channels. Such an experiment will improve the constraints of the neutrino
lifetime $\tau_3$. Compared with exclusion limits in the current accelerator
neutrino experiments T2K and NOvA under the stable $\nu$ assumption, we expect
that MOMENT gives the bound of $\tau_3/m_3\ge1.46\times10^{-11}$~s/eV at
$3\sigma$ confidence level, which is better than their recent limits:
$\tau_3/m_3\ge 7\times10^{-13}$~s/eV in NOvA and $\tau_3/m_3\ge
1.41\times10^{-12}$~s/eV in T2K. The non-decay scenario is expected to be
excluded by MOMENT at the $>3\sigma$ confidence level, if the best fit results
in T2K and NOvA are confirmed. We further find that reducing systematic
uncertainties is slightly more important than the running time. Finally, we
find very little correlations between $\tau_3/m_3$ and other oscillation
parameters, which point to an advantage of MOMENT to measure $\tau_3/m_3$.
