  After several gravitational wave transients were discovered since 2015,
studying neutrino signals coincident with the gravitational wave events now
becomes an important mission for the existing neutrino experiments.
Unfortunately, no candidate neutrinos have been found yet. This article
introduces a method to find the neutrino excess to search for the potential
neutrinos from gravitational wave sources at the future reactor neutrino
experiment (such as JUNO and RENO-50). According to our calculations and
simulations, the non-detection of $\bar\nu_e$ associated with gravitational
waves at the nominal JUNO experiment gives rise to the $\bar\nu_e$ signal
sensitivity at 90$\%$ confidence level (C.L.), $\mu_{90}$ = 2.44. This
corresponds to the range of neutrino fluence on the Earth around 6 $\times$
10$^{10}$ cm$^{-2}$ to 4 $\times$ 10$^{10}$ cm$^{-2}$ with neutrino energy
range from 1.8 MeV to 120 MeV at monochromatic energy spectrum assumption.
Based on certain popular models which describe the gravitational wave sources,
we calculate the corresponding fluence ($F_{UL}^{90}$), which is around 1 - 3
$\times$ 10$^{8}$ cm$^{-2}$ for both monochromatic energy spectrum assumption
and Fermi-Dirac energy spectrum assumption. Then we convert $F_{UL}^{90}$ into
the detectable distance ($D_\text{UL}^{90}$), about 1 - 3 Mpc for two
assumptions, with the predicted luminosities in these known models. To further
improve the sensitivity, we discuss the potential benefits from an extra
detector, with different target masses and baselines. Particularly, there will
be around 38\% sensitivity improvement and around 28$\%$ detectable distance
increasing if the extra detector is designed to be identical to the JUNO
detector. On the other hand, instead of building an extra detector, if we
combine the JUNO experiment with the RENO-50 experiment, the sensitivity will
also be significantly improved.
