The torsional vibration is a subject that should be concerned in a rotating shaft system because it effects on system performance. Therefore, to reduce the transmission of torsional vibration, many researchers have researched until now. In this paper, a novel torsional vibration isolator with Negative-Stiffness Structure (NSS) is presented. The proposed vibration isolator which has the nonlinear stiffness characteristics consists of a linear torsional spring and two pre-compressed springs which provide torsional negative stiffness. To investigate an efficiency of proposed system, an analytical model is developed using the Lagrange’s method and the frequency response curves (FRCs) are calculated by using Harmonic Balance Method (HBM). The results show that the torsional vibration isolation performance of proposed model has improved compared with linear vibration isolator especially in low frequency ranges.