An apparatus for cutting off dark current, and a method of controlling the apparatus are provided. The apparatus for cutting off dark current includes: a communicator to receive an input signal of a remote keyless entry (RKE) remote control from a body control module (BCM); a controller to determine whether the received input signal of the RKE remote control satisfies conditions for changing a dark current control mode of the apparatus, and to send out a control signal to change the dark current control mode upon determination that the input signal of the RKE remote control satisfies the conditions for changing the dark current control mode; and a switch to maintain the changed dark current control mode based on the sent out control signal.