Volatile organic compound (VOC) gases can act as biomarkers for early-stage cancer detection. For this purpose, the detection of VOCs at low ppm levels is critical. To achieve this goal, this study presents a surface acoustic wave (SAW)-based VOC sensor with a composite nanostructure consisting of carbon nanotubes (CNT) and molybdenum disulfide (MoS2) as sensing material. The gas-sensing performance of two models based on CNT and CNT-MoS2 sensing layers was investigated for ten types of VOCs at levels of 10–100 ppm at room temperature. The 2D SAW sensor model was designed and analyzed using the finite-element method (FEM)-based COMSOL Multiphysics 6.0 software. These two-port SAW devices were constructed using a 128° Y-cut LiNbO3 substrate with aluminum as interdigital transducers (IDTs). In the first model (M1), CNT was used as a sensing layer with a resonant frequency of 905.27 MHz, and the second model (M2) used a CNT-MoS2 sensing layer with a resonant frequency of 901.89 MHz. The shift in the resonant frequencies and their respective sensitivity with the presence of VOC gases was calculated. The greatest shift in frequency among gases in both models was found for 2-propanol, with 724.1 Hz/ppm for M1 and 1605.5 Hz/ppm for M2. In addition, the composite device M2 displayed superior selectivity (1630.1 Hz/ppm) to ethanol. The higher sensitivity of M2 may be due to the efficient adsorption of VOC gas molecules on the surface of the CNT-MoS2 nanocomposite, which has a larger specific surface area and provides more active sites, resulting in a greater change in the device resonant frequency due to the mass loading effect.