China Jinping Underground Laboratory (CJPL) is ideal for carrying out MeV-scale neutrino experiments and searching for neutrinoless double-beta-decay. To understand the cosmogenic background, we analyzed 820.28 days of the dataset from a one-ton prototype detector and measured the cosmic-ray muon flux to be (3.61+-0.19stat.+-0.10sys.)*10^-10 cm^-2 s^-1. From the detected cosmic-ray muon events, we also measured the muon-induced neutron yield in liquid scintillation, which is (3.44+-1.86stat.+-0.76sys.)*10^-4 mu^-1 g^-1 cm^2 at 340 GeV average energy of muons. In addition, we performed a survey of muon fluxes at different laboratory locations globally, considering both those situated under mountains and those down mine shafts. Under the same vertical overburden, the former is generally (4+-2) times the latter due to the leakage through the mountain. Based on Jinping Mountain's terrain and the measurement in CJPL-I, we predicted cosmic-ray muons' energy and angle distributions and fluxes for the four halls at CJPL-II. We found the fluxes of Hall C and Hall D were about 2.3*10^-10 cm^-2 s^-1 and 2.5*10^-10 cm^-2 s^-1 respectively.