The present paper analyzes the anomalous scattering from a slightly random surface, a phenomenon similar to Wood's anomalies on optical gratings; the anomaly appears as the rapid variations of the coherently reflected and the incoherently scattered power against the angle of incidence. To clarify the physical mechanism of such anomalous scattering, this paper deals with the two-dimensional case, such that a TM plane wave is incident on the perfectly conductive Gaussian random surface. By a probabilistic method a stochastic wave solution involving multiple scattering is obtained and is shown to have a pole and a zero on the complex wave number plane. The complex pole and zero represent the existence of the guided complex wave (leaky wave) propagating along the random surface. It is concluded that the anomalous scattering is physically caused by the existence of the guided complex wave and can occur strongly in the case of a slightly rough and gently sloping surface. Several properties of the scattering are illustrated in the figures, such as the amplitude and the phase of the coherent reflection, the variance of the wave field, the optical theorem, the angular distribution of the incoherent scattering, and the backscattering cross section.