Method for controlling hybrid power train of vehicle

A method of controlling a power train apparatus of a vehicle, the method comprising:

• while a second input shaft connected to a first motor-generator is operated by the first motor-generator to allow the vehicle to travel in an electric vehicle (EV) mode, driving, by a controller, a first input shaft connected to a second motor-generator by the second motor-generator to synchronize a speed of a predetermined driven gear of a target gear position with a speed of an output shaft;
• primarily moving, by the controller, a sleeve to directly connect the second input shaft, the output shaft, and the driven gear of the target gear position;
• decreasing, by the controller, torque of the first motor-generator and increasing torque of the second motor-generator to converge torque transferred from the second motor-generator to the output shaft, to torque of the output shaft;
• secondarily moving, by the controller, the sleeve to release the second input shaft and maintain the output shaft and the driven gear of the target gear position to be directly connected;
• and
• increasing, by the controller, torque of an engine connected to the first input shaft and decreasing the torque of the second motor-generator to converge torque transferred from the engine to the output shaft, to the torque of the output shaft.