Provided is a hybrid electric vehicle that includes a turbocharger and a method for controlling driving of the hybrid electric vehicle accordingly. In particular, an engine and a motor are configured to generate power respectively. An engine clutch may be positioned between the engine and the driving motor to engage and disengage the engine and the driving motor. An integrated starter and generator (ISG) starts the engine or generates power, and a turbocharger is provided therein. A decelerator adjusts revolution speeds and torque of the turbine and the air compressor of the turbocharger and the integrated starter and generator between the turbine and the air compressor of the turbocharger and the integrated starter and generator. Finally, a controller controls the integrated starter and generator, the engine clutch, the turbo charter, and the decelerator based on states of the engine, the driving motor, and the battery accordingly.