The model-resolution sensitivity of simulated intensifying and deepening rates of an extremely intense tropical cyclone (TC), Typhoon Ida (1958), was investigated using the Japan Meteorological Agency/Meteorological Research Institute nonhydrostatic atmospheric model with horizontal resolutions of 20, 10, 5, and 2 km. The results revealed great differences in the intensifying and deepening rates and their associated structural changes among simulations. The typhoon simulated by a finer horizontal resolution resulted in a greater maximum intensity associated with more rapid intensification. The differences were also revealed in the hourly precipitation pattern, the radius of maximum wind speed at 2-km altitude (RMW) and its shrinking behavior, near-surface inflow, and the axisymmetrization of the inner core. Only the cloud-resolving 2-km model, with explicit microphysics, could reproduce the observed maximum intensity and extreme intensification rate of the typhoon realistically because the model could produce the deep, intense, and upright updrafts inside RMW around the vorticity-rich area over the strong near-surface inflow. The results suggest that the appropriate horizontal resolution of the model should be used in dynamical downscaling experiments to examine extremely intense TCs with extremely high intensifying rates.