The invention discloses a driving system of a double-motor hybrid power electric automobile. A separation and reunion transmission device of the driving system comprises a friction plate type clutch, a stator winding and a rotor winding. A flywheel of the clutch is connected with a clutch cover, the outer side of the clutch cover is connected with a rotor winding iron core, each salient pole of the rotor winding is provided with a winding wire, the winding wires of all the salient poles constitute a bundle, the two ends of the bundle are fixed to two parallel slip rings, the two slip rings are arranged outside a shaft sleeve in a sleeving mode, the shaft sleeve is further connected with the inner circular face of the iron core, the two slip rings are each connected with a brush, the two brushes are connected with a positive pole and a negative pole of an excitation power source fixed to the inner side of a clutch shell respectively, the inner side of the clutch shell is connected with a stator winding iron core, the stator winding is a three-phase stator winding matched with the salient pole rotor winding, and the other ends of three bundles of wires are connected with an accumulator through rectifiers. By means of the driving system, the axial dimension of a parallel connection hybrid power system and the rotational inertia of the output end of an engine can be reduced.