We describe a new method for estimating the beam range in heavy-ion radiation therapy by measuring the ion beam bremsstrahlung. We experimentally confirm that the secondary electron bremsstrahlung process provides the dominant bremsstrahlung contribution. A Monte Carlo simulation shows that the number of background photons from annihilation gamma rays is about 1% of the bremsstrahlung strength in the low-energy region used in our estimation (63-68 keV). Agreement between the experimental results and the theoretical prediction for the characteristic shape of the bremsstrahlung spectrum validates the effectiveness of our new method in estimating the ion beam range.