Previous models on coevolution mostly considered quantitative traits, but recent empirical studies found that Mendelian inheritance is pervasive in ecologically important traits. Moreover, the existence of an antagonistic interaction mediated by continuous quantitative and discrete Mendelian traits was indicated in a predator-prey system with right-handed snakes and left-handed snails. Here I theoretically examined consequences of antagonistic coevolution between predator and prey with quantitative and Mendelian traits. I found that the Mendelian trait of prey can cause extinction of predator, especially when the trait shows complete dominance instead of semidominance. Increasing heritability of the predator traits promotes rapid adaptation, but it can result in chaotic dynamics as well as extinction of predator, which are not common in coevolutionary dynamics between quantitative traits. My study illustrates the importance of revealing genetic bases of ecological traits to understand population and evolutionary dynamics.