A research has been carried out on the effects of different rubber hardness on the parameters of the hyperelastic constitutive model and the stiffness of rubber spring by using the Mooney-Rivlin superelastic constitutive model. A simulation experiment has been conducted on the vertical stiffness of conical rubber spring, followed by a comparison made between the simulation results and the test results of spring stiffness, which shows that the stiffness of rubber exerts a significant influence on the stiffness of rubber spring. The least square method has been adopted to fit the existing discretization data, thus obtaining the function relation between the parameters of the hyperelastic constitutive model and the hardness of the rubber compound. By adopting the orthogonal test method, a simulation test of the stiffness of the conical rubber spring has been carried out, obtaining the value of the best hyperelastic constitutive model corresponding to the hardness of the rubber compound, namely C10=0.312, C01=0.087. The relative error of the simulation stiffness value of the conical spring and the test stiffness turns out to be as low as 0.3%, verifying its high precision.