This work addresses the issue of finding ellipsoidal bounds of reachable sets for neutral semi-Markovian jump systems with time-varying delay and bounded peak disturbances, for which the related result has been rarely proposed for neutral semi-Markovian jump systems. Based on the modified improved Lyapunov-Krasovskii functional, a boundary of the reachable set for neutral semi-Markovian jump systems was obtained with the aid of utilizing a novel integral inequality and combining with the time-delay segmentation technique. The numerical examples are supplied to verify the effectiveness of the obtained results.