As a promising model for the X-ray emission from radio-quiet quasars and Seyfert 1 nuclei, we present a nonthermal disk-corona model, where soft photons from a disk are Comptonized by the nonthermal electron-positron pairs in a coronal region above the disk. Various characteristics of our model are qualitatively similar to the homogeneous, spherical, nonthermal pair models previously studied, but the important difference is that in our disk-corona model gamma-ray depletion is far more efficient, and, moreover, the gamma-ray annihilation line is much less prominent. Consequently, this model naturally satisfies the observed constraints on active galactic nuclei.