  Solar, terrestrial, and supernova neutrino experiments are subject to
muon-induced radioactive backgrounds. The China Jinping Underground Laboratory
(CJPL), with its unique advantage of a 2400 m rock coverage and long distance
from nuclear power plants, is ideal for MeV-scale neutrino experiments. Using a
1-ton prototype detector of the Jinping Neutrino Experiment (JNE), we detected
343 high-energy cosmic-ray muons and (7.86$ \pm $3.97) muon-induced neutrons
from an 820.28-day dataset at the first phase of CJPL (CJPL-I). Based on the
muon-induced neutrons, we measured the corresponding muon-induced neutron yield
in a liquid scintillator to be $ (3.44 \pm 1.86_{\rm stat.}\pm 0.76_{\rm
syst.})\times 10^{-4}\mu ^{-1}\rm g^{-1}cm^{2} $ at an average muon energy of
\SI{340}{GeV}. We provided the first study for such neutron background at CJPL.
A global fit including this measurement shows a power-law coefficient of (0.75$
\pm $0.02) for the dependence of the neutron yield at the liquid scintillator
on muon energy.
