This research involved a 3D simulation of a non-destructive test to detect fluorescence X-rays with a position-sensitive CdTe detector. Simulations were performed under various conditions and on different types of phantoms. All simulations were based on fluorescence X-ray computed tomography (FXCT) using a Monte Carlo method. In general, conventional computed tomography (CT) analyzes materials based on their attenuation coefficients, and is highly dependent on the densities of the materials; hence, discriminating between materials of similar density can be difficult, even if their atomic numbers differ. In this research, the material was exposed to an X-ray source, and the characteristic X-ray was measured by using a 2-dimensional (2D) CdTe planar detector array and was then used to reconstruct a 3-dimensional (3D) image. A 2D CdTe pixelated array has a large detection area and operates with a compact cooling device. Because atoms have their own characteristic X-ray energy spectra, our system was even able to discriminate between materials with similar densities, provided the materials were composed of elements with different atomic numbers. In this research, FXCT was applied to distinguish between various materials, and real-world simulations were performed to verify the feasibility of our system for non-destructive inspection applications.