Accumulator fuel injection system controller and control method and accumulator fuel injection system

To provide an accumulator fuel injection system that can maintain a rail pressure equal to or greater than an injectable pressure for a relatively long time while an internal combustion engine is automatically stopped. An accumulator fuel injection system controller capable of executing idling stop control of an internal combustion engine is equipped with fuel injection valve controlling means that causes fuel injection valves to stop fuel injection after the establishment of an idling stop condition and causes the fuel injection valves to resume fuel injection after the establishment of a restart condition, and rail pressure controlling means that regulates the pressure inside a common rail on the basis of a calculated target rail pressure, wherein the rail pressure controlling means sets the target rail pressure after the establishment of the idling stop condition to a value that is larger than the target rail pressure at the time of the establishment of the idling stop condition.