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Knowledge of electron densities for materials is important for treatment planning for proton and heavier-ion radiotherapy. In order to obtain the electron densities with high precision, we have developed dual-energy X-ray computed tomography using synchrotron radiation. Two monochromatic X-rays with different energies generated from synchrotron radiation enables tomographic imaging which produces a cross sectional image based on electron density plus an additional image based on effective atomic number. Experiments for the dual-energy X-ray CT were made on the BL20B2 beamline at SPring-8. An image intensifier system and a CCD camera were used as the 2-D detectors. The measured electron densities were agreement to within 2% of the theoretical ones. Electron density and effective atomic number provide different contrast in images. Dual-energy X-ray CT can be used for quantitative measurement of the material.