A Fast ignition Advanced Laser fusion reactor CONcept with a Dry first-wall and a high repetition laser (FALCON-D) has been proposed to investigate the potential of the fast ignitionin the reactor concepts. For the blanket system, two types of blanket concepts, i.e.asolid and a liquid metal breeder types using the reduced activation ferritic steel (F82H) were proposed.In this study, two types of blankets were designed, where the thickness of the blankets was minimized while keeping the net TBR larger than 1.07. One of the blanket concepts for FALCON-D is based on the solid breeder (Li2TiO3) with beryllium (Be) neutron multiplier and water cooling. The second blanket concept is based on liquid metal breeder (Li17Pb83) with water cooling. The maintenance method for FALCON-D is applicable to both blanket types. The net electric power of the solid breeder blanket is 110 MW larger than that of the liquid metal breeder blanket. This is mainly caused by the differences in the neutron energy multiplication. In the case of the liquid metal breeder blanket with water cooling, the net TBR 1.09 is achieved without Be as the neutron multiplier. Such design without Be can remove a risk of accident due to the chemical reaction between beryllium and water. From the economical point of view, the solid breeder blanket with water cooling, which generates a larger electric power, is desirable. On the other hand, if the combination of beryllium and water cooling was not acceptable from a viewpoint of safety, the blanket system with the liquid metal would be another possible option.