Hybrid simulation with model updating utilizes the test data to identify the parameters of the experimental substructure and updates the model of the numerical substructure, effectively avoiding the errors induced by the inaccurate parameters of the numerical substructure in traditional hybrid simulation. To ensure the accuracy of parameter identification, the selected constitutive parameters must be observable and highly sensitive. The existing local parameter sensitivity analysis method belongs to qualitative analysis and cannot specifically and quantitatively evaluate the sensitivity of the parameters. Therefore a parameter sensitivity analysis method based on correlation analysis is put forward. This method quantitatively evaluates the parameter sensitivity of constitutive parameters by calculating the correlation coefficient between constitutive parameters and restoring force, and the calculation is simple. The parameter sensitivity analysis of concrete employing the Kent-Scott-Park constitutive model and the composite damper using the trilinear constitutive model is conducted respectively, and the results are compared with those obtained by the local parameter sensitivity analysis method. The results show that the higher sensitivity parameters selected by the two methods for the constitutive parameters of concrete are consistent, while the local parameter sensitivity analysis method is not suitable for the composite damper. The proposed method can determine the parameter sensitivity of the constitutive parameters of the composite damper. A six-story steel frame structure equipped with a composite damper was subjected to a hybrid simulation with model updating numerical simulation using different model update methods. The effects of parameter identification were compared and it was found that the constitutive parameters selected by the proposed method were easier to identify, and the hybrid simulation with model updating numerical simulation had higher accuracy and efficiency, which verified the correctness and effectiveness of the method.