For ion beam radiation therapy, the measurement of effective atomic numbers is necessary to know the material distribution in a human body: the range of ion beams entering the human body is influenced by the material distribution along their paths. Effective atomic numbers, however, cannot be measured at hospitals because monochromatic X-rays with different energies are necessary and are used only at synchrotron facilities. To make the effective atomic number measurements at hand, we propose energy-resolved computed tomography (CT) using a "transXend detector". By assigning two narrow energy ranges in the unfolding process of the data obtained by the transXend detector, the effective atomic numbers for acrylic and aluminum can be estimated by energy-resolved CT. The estimated effective atomic numbers are compared with those obtained by dual-energy and monochromatic X-ray CT.