The China Jinping Underground Laboratory (CJPL), which has the lowest cosmic-ray muon flux and the lowest reactor neutrino flux of any laboratory, is ideal to carry out low-energy neutrino experiments. With two detectors and a total fiducial mass of 2000 tons for solar neutrino physics (equivalently, 3000 tons for geo-neutrino and supernova neutrino physics), the Jinping neutrino experiment will have the potential to identify the neutrinos from the CNO fusion cycles of the Sun, to cover the transition phase for the solar neutrino oscillation from vacuum to matter mixing, and to measure the geo-neutrino flux, including the Th/U ratio. These goals can be fulfilled with mature existing techniques. Efforts on increasing the target mass with multi-modular neutrino detectors and on developing the slow liquid scintillator will increase the Jinping discovery potential in the study of solar neutrinos, geo-neutrinos, supernova neutrinos, and dark matter.