A floating type backward-bent duct buoy (BBDB) is a wave energy conversion device with an oscillating water column (OWC) at the front side. The device captures the wave energy using the heaving, the pitching, the surging motion of BBDB, and the heaving motion of OWC. Investigations are carried out to find more reasonable devices than the traditional OWC type floating device. An eigenfunction expansion method is introduced for analyzing the BBDB with OWC. It is confirmed that these solutions give good agreement with several experimental results in this paper. It is shown in a design method how to make BBDB match the turbine characteristics. This feature is being able to select the optimum profile of the turbine and the BBDB individually from each characteristic before comprehensive evaluation of the BBDB and the turbine in the design. After grasping the element characteristics, which are appropriate for the wave energy conversion system, the synthetic design method is built. The BBDB size and the turbine diameter are determined by considering the cost corresponding to the smallest size under the same output. In this way, we can obtain the optimal profiles considering the construction cost including the turbines.