Solar-, geo-, and supernova neutrino experiments are subject to muon-induced radioactive background. China Jinping Underground Laboratory (CJPL), with its unique advantage of 2400 m rock coverage and 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 (6.24$ pm $3.66) 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 neutron yield in liquid scintillator to be $(3.13 pm 1.84_{rm stat.}pm 0.70_{rm syst.})times 10^{-4}mu ^{-1}rm g^{-1}cm^{2}$ at an average muon energy of 340 GeV. This study provides the first measurement for this kind of 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 liquid scintillator on muon energy.
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