The invention provides a motor drive assembly and a torque transmission mechanism thereof. The motor drive assembly includes a single-phase motor and a torque transmission mechanism. The torque transmission mechanism includes a driving member driven by the motor, a driven member for driving a load to rotate in one direction, and a connecting device. The connecting device comprises an elastic member and a vibration-absorptive material. One end of the elastic member is connected to the driving member and the other end of the elastic member is connected to the driven member. The vibration-absorptive material coats or sleeves the elastic member or the gaps of the elastic member are filled with the vibration-absorptive material, or the elastic member is directly made of the vibration-absorptive material to reduce the noise generated by the elastic member. The motor drive assembly has a buffering effect on the motor to drive a heavy load, prevents the motor from failing to start and from being damaged, and effectively reduces the noise generated by the elastic member.