A transmission unit for a vehicle includes: a plurality of input shafts (11, 12), each of the input shafts (11, 12) provided with a shift driving gear (la-5a); a plurality of output shafts (21, 22), each of the output shafts (21, 22) being provided with a shift driven gear (lb-5b) configured to mesh with a corresponding shift driving gear (la-5a); a motor power shaft (3); first and second motor gears (31, 32) freely fitted over the motor power shaft (3); a motor synchronizer (33c) disposed on the motor power shaft (3) and between the first and second motor gears (31, 32); the first motor gear (31) is configured to rotate together with one of the input shafts (11, 12); the second motor gear (32) is configured to rotate together with one of the output shafts (21, 22). A power transmission system and a vehicle are also provided.