A shooting game apparatus includes an LCD for displaying a target and an operating button for a player to perform operation of shooting the target. For example, an enemy character is switched between an ineffective state in which it is never damaged even if an attack hits it and an effective state in which it is damaged if an attack hits it. Different images are displayed depending on whether the target is in the ineffective state or in the effective state. In case where the target is in the effective state, when a player character enters into a state of being continuously damaged because it is positioned in such an area as it receives continuous damage, for example, the target is switched into the ineffective state.