Abstract A torsion vibration isolator with quasi-zero stiffness (QZS) is proposed to attenuate the transmission of torsional vibration along a shaft system, which also plays a role of coupling between shafts. A pre-compressed cam–roller mechanism is designed to provide torsional negative stiffness that counteracts with the positive torsion stiffness of the vulcanized rubber between shafts. With the design parameters are set to satisfy a unique condition, the stiffness of the isolator delivers a QZS property about the equilibrium position. A nonlinear mathematical model is developed and its dynamic characteristics are further analyzed by using the Harmonic Balance method. A typical folded resonance curve occurs when the vibration amplitude is plotted as the excitation frequency is varied, illustrating a jump phenomenon in the response. The efficiency of vibration attenuation is estimated under a designed torque load, showing that the torsion QZS vibration isolator outperforms the corresponding linear counterpart, especial in low frequency ranges. Furthermore, the torque transmissibility of the QZS isolator is also studied to demonstrate the performance of the QZS isolator when the actual torque deviates from the design load.