The present invention provides an apparatus and method for controlling the operation of an electric oil pump for creating a working fluid pressure in a transmission and a clutch for a hybrid vehicle, which can accurately reflect the viscosity characteristics of oil to accurately control the operation of the pump, instead of measuring the temperature of the oil to reflect the state of the oil. In preferred embodiments, the present invention provides an apparatus for controlling the operation of an electric oil pump, the apparatus including: a current detector for detecting a current applied to a motor of an electric oil pump; a rotational speed detector for detecting a rotational speed of the motor; and a controller for calculating a load torque of the motor based on the detection values of the current detector and the rotational speed detector, calculating a target rotational speed based on the detection values, and controlling the operation of the motor based on the target rotational speed.