In the preparation of carbon dots (CDs), precursors are crucial, and abundant precursors endow CDs with various structures and fluorescence characteristics. Furan (FU) and its derivatives are considered excellent carbonization materials due to their π conjugated structures and active functional groups, such as hydroxyl and aldehyde groups. Herein, we prepare FU-derivative-based CDs by a solvothermal method and investigate the influences of the precursor structure on the fluorescence characteristics. Surprisingly, CDs prepared from 5-hydroxymethylfurfural (HMF) with both aldehyde and hydroxyl groups exhibit red-shifted fluorescence characteristics in the solid state. We postulate that this solid-state fluorescence characteristic is due to the enhancement of supramolecular cross-linking fluorescence between CDs. The unique precursor structure leads to carboxyl groups on the surface of HMF-CDs that are conducive to the hydrogen bond formation. As the concentration of CDs increases, the hydrogen bonding effect increases, leading to a red-shift in the fluorescence wavelength. Therefore, basically full-color CDs/poly(vinyl alcohol) (PVA) phosphor-based light-emitting diodes can be achieved by controlling the degree of supramolecular cross-linking of CDs in PVA. This research provides a new approach for the preparation of solid-state luminescent CDs.