Acetone is a slightly toxic volatile organic gas, which exists in the breath and is closely related to diseases such as diabetes. In this paper, a quartz crystal microbalance (QCM) was used to fabricate an acetone sensor, and graphene quantum dots (GQDs) were used as a gas-sensing material to modify the QCM. GQDs were prepared by citrate pyrolysis and characterized by high-resolution transmission electron microscopy (TEM). The gas sensitivity of the sensor to low concentrations of acetone was investigated. It exhibited good linearity at acetone concentrations of less than 240 ppm with a sensitivity of 16.78 Hz/ppm and a minimum detection limit of 2.5 ppm, and the fitted line had a coefficient of determination R2 of 0.95658. In a mixture of acetone, butanol, and isopropanol, the sensor exhibited good selectivity for acetone. For different acetone concentrations, the response speed of the same sensor was basically the same, and the response and recovery times were 32 and 48 s, respectively. We showed that the prepared gas sensor has good sensitivity, repeatability, and selectivity for low concentrations of acetone.