The invention discloses a hybrid-electric-vehicle driving system good in dynamic matching and shift smoothness. The hybrid-electric-vehicle driving system is characterized in that a crankshaft of a motor is sequentially connected with a coupling clutch, a connecting shaft and a planet frame of a planet gear train from right to left, the right end of a motor shaft of a driving motor is fixedly connected with a sun gear, a second driving gear, a second clutch, a first clutch and a first driving gear are located between the planet gear train and the coupling clutch and are arranged sequentially from left to right, the second driving gear and the first driving gear are sleeved on the connecting shaft to be respectively meshed with a second passive gear and a first passive gear, an external drum of the second clutch and an external drum of the first clutch are connected with the connecting shaft while an internal drum of the second clutch and an internal drum of the first clutch are respectively connected with the second driving gear and the first driving gear or the internal drum of the second clutch and the drum of the first clutch are connected with the connecting shaft while the external drum of the second clutch and the external drum of the first clutch are respectively connected with the second riving gear and the first driving gear, a constant mesh gear, the second passive gear and the first passive gear are sequentially arranged on the output shaft from left to right and are all fixedly connected with the input shaft, and an external gear ring is fixedly connected with the gear ring of the planet gear train and are meshed with the constant mesh gear.