A method has been developed to estimate the irradiation history and burnup of a spent fuel by gamma-ray spectroscopy. The gamma-ray spectrum, measured by using a Ge(Li) detector, is analyzed by the standard spectrum method to obtain the activity of the fission product. The irradiation history is fitted by the least-squares method to reproduce the activity of each fission-product nuclide. For this purpose, the irradiation history is divided into several time intervals and the contribution of each interval to the production of each fission product is calculated analytically by repeatedly using the Bateman equation. The method was successfully applied to the Materials Testing Reactor-type fuel element irradiated in the core of Japan Research Reactor-4 for about four years.