Three-dimensional (3D) radiated sound field display systems are important toward realizing ultra-realistic communications systems such as 3D television. In this paper, a 3D radiated sound field display system using directional loudspeakers and wave field synthesis is proposed. The proposed system is based on the Fresnel-Kirchhoff diffraction formula, which is the approximate form of the Kirchhoff-Helmholtz integral equation. The proposed system was developed by constructing the surrounding microphone array and radiated loudspeaker array. To evaluate the performance of the developed system, the positions of sound images were estimated. The results indicated that the 3D sound field is accurately controlled outside of the radiated loudspeaker array by sharpening the radiation directivity of the loudspeaker units and that the sound images are not correctly estimated in the developed system because the radiation directivity of loudspeaker units is not sufficiently sharp.