To perform low-dose low-scattering X-ray computed tomography (CT), we have constructed a dual-energy (DE) X-ray photon counter with a high-count-rate detector system and energy-range and -region selectors. The detector system consists of a cerium-doped yttrium aluminum perovskite [YAP(Ce)] crystal, a small photomultiplier tube (PMT), and an inverse amplifier for the PMT with a pulse-width extender. In DE-CT, both the X-ray source and the detector module are fixed, and the object on the turntable oscillates on the translation stage. A line beam for DE-CT is formed using a two lead (Pb) pinholes in front of the object. The scattering-photon count from the object is reduced using a Pb pinhole behind the object. To improve the spatial resolution, a 0.5-mm-diam Pb pinhole is attached to the YAP(Ce)-PMT detector. X-ray photons are detected using the detector system, and the event pulses are input to the two energy selectors. In DE-CT, the tube voltage and the maximum current were 100 kV and 0.60 mA, respectively. The energy range and region for soft and gadolinium-K-edge CT are 20-40 and beyond 50 keV (50-100 keV), respectively. The maximum count rate of DE-CT was 84 kilocounts per second, and the exposure time for tomography was 19.6 min at a total rotation angle of 360°.