To provide an apparatus and method for controlling the driving of a hybrid electric vehicle on a slope for increasing a traveling distance by an electric motor, and for improving fuel consumption by preventing the abrupt generation of motor torque while traveling on the slope, and also by preventing battery discharge due to the generation.

While a hybrid electric vehicle travels on a slope, one mode selected from an engine traveling mode, a motor traveling mode, and an engine-motor combined traveling mode is executed according to a battery state of charge and a degree of the slope to increase a traveling distance by a motor by preliminarily preventing the abrupt generation of motor torque while traveling on the slope. Thus, the traveling distance by the motor is increased, and the start of an internal combustion engine is minimized so as to improve fuel consumption.