This paper proposes a novel design torsional vibration isolator with negative stiffness structures. It consists of two shafts that are linked by positive springs and negative stiffness structures. The connection position of the two shafts has been designed into disc structure, which is the installation position of the positive springs and negative stiffness structures. The task of positive springs is to transmit the designed torque. In this paper, the nonlinear stiffness characteristics of the isolator are presented. The nonlinear mathematical model is presented, and its dynamic behaviors are investigated using the averaging method, and compared with that of the corresponding linear torsion isolator without negative stiffness structures. The study shows that the torsion isolator has a wider isolation region than that of the linear isolator. Furthermore, the performance of the isolator is sensitive to the damping of the system and the amplitude of vibration excitation. Choosing a suitable damping and vibration environment will be important for the stable application of this isolator.