The thickness of the sensitive layer has an important influence on the sensitivity of a shear horizontal surface acoustic wave (SH-SAW) biosensor with a delay-line structure and lower layer numbers of graphene produce better sensitivity for biological detection. Therefore, a label-free and highly sensitive SH-SAW biosensor with chemical vapor deposition (CVD-)-grown single-layered graphene (SLG) for endotoxin detection was developed in this study. With this methodology, SH-SAW biosensors were fabricated on a 36°Y-90°X quartz substrate with a base frequency of 246.2 MHz, and an effective detection cell was fabricated using acrylic material. To increase the surface hydrophilicity, chitosan was applied to the surface of the SLG film. Additionally, the aptamer was immobilized on the surface of the SLG film by cross-linking with glutaraldehyde. Finally, the sensitivity was verified by endotoxin detection with a linear detection ranging from 0 to 100 ng/mL, and the detection limit (LOD) was as low as 3.53 ng/mL. In addition, the stability of this type of SH-SAW biosensor from the air phase to the liquid phase proved to be excellent and the specificity was tested and verified by detecting the endotoxin obtained from Escherichia coli (E. coli), the endotoxin obtained from Pseudomonas aeruginosa (P. aeruginosa), and aflatoxin. Therefore, this type of SH-SAW biosensor with a CVD-grown SLG film may offer a promising approach to endotoxin detection, and it may have great potential in clinical applications.