An apparatus for controlling a construction machine, the apparatus comprising: an electronic joystick configured to generate a request signal; a main controller configured to receive the request signal and generate a torque command and a pilot signal; an engine control unit configured to receive the torque command and generate an engine revolutions per minute command; an engine configured to operate in compliance with the engine RPM command; a hydraulic pump/motor configured to be operated by the engine and discharge a working fluid or to be driven by an incoming working fluid and output power; a main control valve controller configured to receive the pilot signal and control an electronic proportional control valve configured to control a working device; and an auxiliary power device configured to be additionally installed on the engine or hydraulic pump/motor and provide auxiliary power to the engine or hydraulic pump/motor; wherein a fuel efficiency map is installed on the main controller or the engine control unit; wherein the fuel efficiency map includes a plurality of torque curves for engine RPMs and fuel efficiency curves for engine RPMs which are set according to various conditions; and wherein the main controller or the engine control unit, when the auxiliary power is provided by the auxiliary power device, is arranged to decrease the engine RPM, or to change a current torque curve to a torque curve corresponding to a condition in which the auxiliary power is provided and selected from among the plurality of torque curves and selectively applies the latter torque curve, based on the fuel efficiency map, characterized in that the main controller or the engine control unit is arranged to compare a fuel efficiency gain expected when the engine RPM is decreased with a fuel efficiency gain expected when the current torque curve is changed to the torque curve corresponding to the condition in which the auxiliary power is provided and selected from among the plurality of torque curves and then the latter torque curve is selectively applied, based on the fuel efficiency map, and to control the engine by means of a method by which a larger fuel efficiency gain is expected. an electronic joystick configured to generate a request signal; a main controller configured to receive the request signal and generate a torque command and a pilot signal; an engine control unit configured to receive the torque command and generate an engine revolutions per minute command; an engine configured to operate in compliance with the engine RPM command; a hydraulic pump/motor configured to be operated by the engine and discharge a working fluid or to be driven by an incoming working fluid and output power; a main control valve controller configured to receive the pilot signal and control an electronic proportional control valve configured to control a working device; and an auxiliary power device configured to be additionally installed on the engine or hydraulic pump/motor and provide auxiliary power to the engine or hydraulic pump/motor; wherein a fuel efficiency map is installed on the main controller or the engine control unit; wherein the fuel efficiency map includes a plurality of torque curves for engine RPMs and fuel efficiency curves for engine RPMs which are set according to various conditions; and wherein the main controller or the engine control unit, when the auxiliary power is provided by the auxiliary power device, is arranged to decrease the engine RPM, or to change a current torque curve to a torque curve corresponding to a condition in which the auxiliary power is provided and selected from among the plurality of torque curves and selectively applies the latter torque curve, based on the fuel efficiency map, characterized in that the main controller or the engine control unit is arranged to compare a fuel efficiency gain expected when the engine RPM is decreased with a fuel efficiency gain expected when the current torque curve is changed to the torque curve corresponding to the condition in which the auxiliary power is provided and selected from among the plurality of torque curves and then the latter torque curve is selectively applied, based on the fuel efficiency map, and to control the engine by means of a method by which a larger fuel efficiency gain is expected.