The invention provides a hybrid electric vehicle driving system based on three clutches. The system comprises an engine, a first motor, a second motor and an energy storage mechanism, wherein the engine is in transmission connection with an output end of the first motor through a first planet gear mechanism; the output of the first planet gear mechanism is in transmission connection with a second planet gear mechanism; an output end of the second motor is in transmission connection with the second planet gear mechanism; a first clutch is arranged on a first gear ring; an output end of a first planet carrier is in transmission connection with a second gear ring; the output end of the second motor is in transmission connection with a second sun wheel; a second clutch is arranged between the first planet carrier and the second gear ring; and a third clutch is arranged between a first sun wheel and the first gear ring and is connected with the engine and the output end of the first motor. The hybrid electric vehicle driving system has a simple structure, is easy to industrialize, can realize various working conditions through a finished vehicle, is energy-saving and environment-friendly and has extremely high practicality.