As the crucial reset component of the shearing device for spent fuel, stranded wire helical spring (SWHS) is cylindrical spring wound by a wire rope strand. Compared with the single-wire cylindrical helical springs, SWHS has the advantages of higher reliability, longer fatigue life, larger stiffness, higher compression ratio and reliability because of the unique structure. Hence it can significantly improve the safety, reliability, stability, and flexibility of the spent fuel shearing device. The accurate parametric model of the spring geometry can significantly improve the efficiency and the accuracy of further theoretical and FEM analysis, hence, is critical for the design and manufacture of the spring. However, the widely used double helix parametric geometric model has non-negligible errors and made the interwire contact interactions unpredictable. Hence, the relative movement between the adjacent outside wires, the gradual stiffness mechanism, the control method of spring performance, and the manufacturing springback compensation mechanism cannot be studied with the existing parametric geometric model, making it difficult to guarantee the performance of the spring. To cope with this problem, an improved parametric model is proposed and experiments and simulations are performed in this paper. The study of this paper will provide comprehensive theoretical and technical support for performance rapid subtle regulating and rapid design methods of the high reliable reset SWHS.