Wave reflection control functions of mound for the foundation of composite and perforated break-waters were investigated through the theoretical considerations. The theory developed is based on a simple summation of components of reflected waves. The applicability of the theory is assured by the comparative studies of the theoretical calculation and experimental data on the sea surface elevation in front of a breakwater. It is found that the reflection is mainly controlled by depth and width of the mound. In the design of composite type perforated breakwaters, the width of perforated part of the upright section can be decreased to less than half of the conventional design width for the same reflection by using the reflection control function of mound part and the reflection can be reduced until less than $30\%$ of that in the composite breakwaters. Using the results, a design method of mounds is proposed, by which the reduction of wave reflection is assured under the given wave conditions.