We have presented a simple approach for quantitative phase imaging by optimizing asymmetric illumination of a conventional microscope. With this illumination, the light intensity modulation accompanying refraction at the surface profile of phase objects occurs, and "phase-gradient information" can be derived by detecting it. Two images with phase-gradient information on different axes are converted into the two-dimensional phase distribution of the specimen by introducing the phase-gradient transfer function, which is the intensity change due to refraction by the phase-gradient of a specimen. We experimentally confirm accurate and repeatable performance of our method and demonstrate phase imaging of live cells.