Oscillatory turbulent flow produced near a rough seabed by linear surface waves is analyzed. An analogy to the wall region of steady turbulent flow is shown to be valid very near the bed and provides the basis for a model in which the eddy viscosity is the product of a vertical length scale and the first two Fourier components of a shear velocity based on the instantaneous, local bed shear stress. With this time-varying eddy viscosity model, an approximate closed-form solution for the boundary-layer flow is obtained. Comparison with available laboratory measurements indicates that the eddy viscosity does in fact vary with time and that the theoretical approach taken here is physically sound. The effect of a time-varying viscosity on quantities of practical interest is found to be potentially important.