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Highly fluorescent carbon nanodots (CNDs) have broad application prospects in optoelectronics, energy, biological imaging, and other fields because of their good solubility in water, adjustable photoluminescence (PL), low toxicity, good biocompatibility, and stable chemical properties. In this paper, polyethyleneimine@CNDs (PEI@CNDs) with unique excitation- and concentration-dependent PL properties were synthesized by a one-pot hydrothermal approach. The morphology, structure, surface chemistry, photophysical properties, and stability of the PEI@CNDs were well probed. The PEI@CNDs solution at low concentration displayed blue PL with a quantum yield of 50.6%. As the concentrations of the PEI@CNDs increase, the PL colors changed from blue, cyan, and green, to greenish-yellow. At low concentration, the excitation-independent and excitation-dependent PL property is mainly caused by carbon core and surface state emission. However, at higher concentration, the quenched blue emission and enhanced green emission were found. This is mainly attributed to the aggregate-related inner filter effect, electron transfer, and surface states. Mixing 10.0 mg/mL of PEI@CNDs with polyvinyl alcohol can be used to construct composite films, which were combined with the blue light-emitting diode to construct white light-emitting diodes with white and warm white emissions.