An apparatus and a method for controlling a creep torque of a hybrid electric vehicle that outputs the creep torque to improve shift feel and fuel consumption of the hybrid electric vehicle, may include the method for controlling a creep torque of a hybrid electric vehicle that may include detecting data of the hybrid electric vehicle for controlling the creep torque, determining whether a vehicle speed is greater than or equal to a predetermined speed and the hybrid electric vehicle is shifting from a current shift stage to 1 stage when the current shift stage is 3 stage or 2 stage, applying a creep torque factor depending on a shift stage and a brake amount when the hybrid electric vehicle is shifting from 3 stage or 2 stage to 1 stage, and controlling a motor to output the creep torque to which the creep torque factor is applied.