Craniofacial profile is one of the anatomical causes of obstructive sleep apnea(OSA). By medical research, cephalometry provides information on patients' skeletal structures and soft tissues. In this work, a novel approach to cephalometric analysis using quasi-conformal geometry based local deformation information was proposed for OSA classification. Our study was a retrospective analysis based on 60 case-control pairs with accessible lateral cephalometry and polysomnography (PSG) data. By using the quasi-conformal geometry to study the local deformation around 15 landmark points, and combining the results with three linear distances between landmark points, a total of 1218 information features were obtained per subject. A L2 norm based classification model was built. Under experiments, our proposed model achieves 92.5% testing accuracy.