We developed a quantitative theory of the phonon-drag thermopower for the 2D electron gas in a quantum well with parabolic confinement potential. The temperature gradient is directed across the confinement direction, i.e., along the plane of a two-dimensional electron gas. Our theoretical results are in a good agreement with experimental data [1] in a range of 1-10 K. In this temperature interval, the main contribution to the thermopower comes from phonon-drag.