A facile and straightforward strategy was developed for the fabrication of highly fluorescent carbon quantum dots (CQDs). The CQDs were synthesized only using pure-solvent tetrahydrofuran (THF) as carbon source via a one-step hydrothermal treatment without further surface passivation or modification. The as-synthesized CQDs emitted bright blue fluorescence and showed a strong emission at 460 nm with excitation at 370 nm. Also, the CQDs displayed a high quantum yield of 11.5%. The CQDs not only showed excellent photoluminescence properties and water solubility, but also exhibited an exceptional multifunctional fluorescence sensor for the applications of pH probing and silver ion (Ag+) sensing. There was a linear correlation between the fluorescence intensity vs. the pH value in the range from 4.0 to 12.0 (R2 = 0.987). In addition, the sensor could detect Ag+ (R2 = 0.998) in the concentration range of 0.2–50 μM with a detection limit of 0.075 μM. Furthermore, the proposed method is applicable to the detection of Ag+ in real aqueous samples, which is a detection system with excellent development prospects.