Traditional high-static-low-dynamic stiffness (HSLDs) vibration isolators can effectively mitigate low-frequency micro-amplitude vibrations. However, in practical engineering applications, low-frequency torsional vibrations are often accompanied by large-amplitude vibrations. Due to the nonlinearity of the negative stiffness spring, the isolation performance of these isolators often deteriorates under large-amplitude torsional vibrations. Moreover, due to the constraints of the annular structure, it is challenging to achieve a large linear negative stiffness range while maintaining sufficient negative stiffness without significantly increasing the volume. To address this issue, based on the convex-concave counteraction principle, a novel large linear stroke magnetic negative stiffness torsional spring (LLS-MNSTS) is proposed to construct a large linear stroke high-static-low-dynamic stiffness (LLS-HSLDs) torsional vibration isolator. The LLS-MNSTS is composed of four magnetic rings, which can be divided into a group exhibiting concave negative stiffness and another group exhibiting convex negative stiffness. Firstly, the analytical magnetic stiffness model of the LLS-MNSTS is established through the equivalent model of magnetic forces. The influence of various parameters is investigated to determine its basic structure. Based on the theoretical magnetic stiffness model and parameter analysis, an optimization model is constructed to minimize the variation of the magnetic negative stiffness over a large range centered around the equilibrium position. By solving the proposed optimization problem, the parameters of the LLS-MNSTS are carefully determined. The variation of the convex negative stiffness effectively counteracts the variation of the concave negative stiffness, resulting in an approximately constant resultant magnetic negative stiffness within a stroke range of (−22°, 22°). Moreover, compared with existing traditional magnetic negative stiffness torsional springs, the designed LLS-MNSTS achieves a larger linear stroke under the same negative stiffness and approximate dimensions, as evidenced by the comparative analysis.