An apparatus and a method for controlling driving of a hybrid electric vehicle on a slope are disclosed. With the apparatus and the method, the hybrid electric vehicle travels on the slope in one mode selected from an engine-motor combined driving mode, an engine driving mode, and a motor driving mode according to an SOC of the battery and a degree of the slope. Accordingly, when traveling on the slope, a driving mode can be determined according to the degree of the slope and the SOC of the battery, thereby previously preventing motor torque from being abruptly increased while traveling on the slope. As a result, a travel distance of the electric motor can be increased, and the start of the internal combustion engine is minimized, thereby enhancing the fuel efficiency by reducing the fuel consumption.