It is intended to provide: an electric supercharging apparatus wherein, with a simple structure, rotor windage loss in an electric motor for driving a compressor is reduced and good cooling performance is produced; and a multi-stage supercharging system using the electric supercharging device. This electric supercharging apparatus is provided with: a first cooling passage formed in a stator along a motor coil and communicating a gas supply port with a gas discharge port in a motor housing; and a first intake passage connecting the gas discharge port to an intake port of a compressor. This electric supercharging apparatus is configured to introduce outside air into the first cooling passage via the gas supply port by applying negative pressure to the first cooling passage via the first intake passage, thereby cooling the inside of the motor housing.