Solid-moderated cores of the Kyoto University Critical Assembly (KUCA) have an emergency shutdown system to avoid any reactivity-initiated accidents. When a reactor protection system of KUCA detects some abnormal conditions, the emergency system withdraws downward several fuel and reflector assemblies assigned as a central fuel loading from the core in 10 and several seconds. The withdrawal of the fuel loading inserts a very large negative reactivity into the core. The negative reactivity has been measured by the integral count technique; however, the application of the integral count technique to this measurement must have been impossible in principle. The integral count technique assumes an instantaneous insertion of a large negative reactivity but the assumption must fail for this measurement. An accurate measurement of the negative reactivity is of extreme importance from the viewpoint of reactor safety. In this study, the least-squares inverse kinetics method was employed to determine the negative reactivity from time-sequence counts data of a neutron counter. The negative reactivity determined by this method was in good agreement with that calculated by the continuous-energy Monte Carlo code MVP (version 3) with the nuclear data library JENDL-4.0.