China Jinping Underground Laboratory (CJPL) is ideal for studying solar-, geo-, and supernova neutrinos. A precise measurement of the cosmic-ray background would play an essential role in proceeding with the R&D research for these MeV-scale neutrino experiments. Using a 1-ton prototype detector for the Jinping Neutrino Experiment (JNE), we detected 264 high-energy muon events from a 645.2-day dataset at the first phase of CJPL (CJPL-I), reconstructed their directions, and measured the cosmic-ray muon flux to be $(3.53pm0.22_{text{stat.}}pm0.07_{text{sys.}})times10^{-10}$ cm$^{-2}$s$^{-1}$. The observed angular distributions indicate the leakage of cosmic-ray muon background and agree with the simulation accounting for Jinping mountains terrain. A survey of muon fluxes at different laboratory locations situated under mountains and below mine shaft indicated that the former is generally a factor of $(4pm2)$ larger than the latter with the same vertical overburden. This study provides a convenient back-of-the-envelope estimation for muon flux of an underground experiment.
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