There are no simple singular Whittaker modules over most of important algebras, such as simple complex finite-dimensional Lie algebras, affine Kac–Moody Lie algebras, the Virasoro algebra, the Heisenberg–Virasoro algebra and the Schrodinger–Witt algebra. In this paper, however, we construct simple singular Whittaker modules over the Schrodinger algebra. Moreover, simple singular Whittaker modules over the Schrodinger algebra are classified. As a result, simple modules for the Schrodinger algebra which are locally finite over the positive part are completely classified. We also give characterizations of simple highest weight modules and simple singular Whittaker modules.