We developed a 3D tomographic non-destructive test detecting fluorescence X-rays with a 2D CdTe array. Experiments proceeded with various phantoms and image reconstruction methods. In general, conventional Computed Tomography (CT) analyzes materials based on attenuation coefficients and is highly dependent on the densities of the materials, and hence, it is difficult to discriminate similar density materials even if their atomic numbers is different from each other. In our research, the material was exposed to an X-ray and not only the conventional transmission image but also 3D images based on the information of characteristic X-ray detected by a 2D CdTe planar detector array were reconstructed. Since atoms have their own characteristic X-ray energy, our system was able to discriminate materials of even a same density if the materials were composed of different atomic numbers. In addition, the transmission and characteristic X-ray images were combined to specifically analyze the information of position, density and atomic number on unknown materials. Several image reconstruction methods were applied and the reconstructed images were compared with each other to figure out an algorithm optimized to FXCT.