  We study the \textit{CP} violation in the lepton-number-violating process
$B_s^0 \rightarrow D_s^- \mu^+ \mu^+ \pi^-$ and its \textit{CP}-conjugate
process $\bar{B_s^0} \rightarrow D_s^+ \mu^- \mu^- \pi^+$ that are induced by
two GeV-scale Majorana neutrinos with nearly-degenerate masses. Our result
shows that the size of the \textit{CP} violation could become considerable if
the mass difference between the two Majorana neutrinos is around the decay
width of the neutrinos. We perform experimental analysis on the
\textit{CP}-violating processes at LHCb within its upgrade II. The analysis
shows that under current constraint on the heavy-light neutrino mixing
parameter, it is possible that such \textit{CP} violation is observed with the
LHCb experimental ability. We also give the upper bound on the heavy-light
mixing parameter $|U_{\mu N}|^2$ under the assumption that no positive signal
of the process is observed. The result shows that such modes can give
complementary constraint compared with previous experiments such as NuTeV,
BEBC, etc. in the mass region 1~GeV $< m_N <$ 3~GeV.
