Theoretical and laboratory studies are performed to analyze the wave attenuation phenomenon over fluid mud under current. In the theoretical part, a semi-empirical formula is derived to model the attenuation process under current. Based on the linear wave theory, the change of wave amplitude is related with the averaged damping effect of the muddy bed. By solving a differential equation, the exponential decay of the wave amplitude is confirmed. A function called damping function is used in the formula, and it is expanded into a series of wave parameters and some undetermined coefficients called auxiliary damping factors. Based on the assumption that the mud properties do not change under current, the formula is combined with the dispersion relation for linear wave under uniform current to describe the attenuation process under current. Laboratory experiments are conducted first without current. The data of wave attenuation are collected and inserted to the formula obtained in the theoretical analysis to figure out the values of the auxiliary damping factors. The second set of experiments is conducted under current and the collected data are compared with the calculated values obtained by using the newly proposed formula with the dispersion relation. The result of comparison shows good applicability of the new formula to the wave attenuation under current.