Human cortical gray matter (GM) is structurally asymmetrical and this asymmetry has been discussed to be partly responsible for functional lateralization of human cognition and behavior. Past studies on brain asymmetry have shown mixed results so far, with some studies focusing on the global shapes of the brain's surface, such as gyrification patterns, while others focused on regional brain volumes. In this study, we investigated cortical GM asymmetries in a large sample of right-handed healthy volunteers (n = 101), using a surface-based method which allows to analyze brain cortical thickness and surface area separately. As a result, substantially different patterns of symmetry emerged between cortical thickness and surface area measures. In general, asymmetry is more prominent in the measure of surface compared to that of thickness. Such a detailed investigation of structural asymmetries in the normal brain contributes largely to our knowledge of normal brain development and also offers insights into the neurodevelopmental basis of psychiatric disorders, such as schizophrenia.