Abstract: Bennett linkage in engineering may contain uncertain parameters, and the influence of uncertain parameters need to be considered in its dynamic analysis. In this study, a dynamic analysis method is proposed for Bennett linkage with parameter uncertainties based on Chebyshev polynomials method and finite particle method (FPM). Firstly, the modeling method of Bennett linkage and the corresponding elements of FPM are presented. Subsequently, by introducing Chebyshev polynomials method, the dependence of the system dynamic response on its parameters is established, and the boundaries of dynamic response can be obtained through interval operations. A non-intrusive uncertainty analysis method that can be easily integrated with the FPM is proposed. Finally, the effectiveness of the method proposed is validated by the numerical examples, and the dynamic analysis of Bennett linkage with parameter uncertainties is conducted. The analysis results indicate that the uncertainty in link lengths significantly influences both the displacement response and velocity response of Bennett linkage. The maximum difference between upper and lower displacement boundaries accounts for 87.1% of that of the deterministic parameter model at that particular time. The uncertainty in Young’s modulus of link has a minor impact on the displacement of Bennett linkage but a substantial impact on the velocity and potential energy of link. The maximum difference between upper and lower velocity boundaries accounts for 277.0% of that of the deterministic parameter model at that particular time. Strong external forces, such as the contact between adjacent links, can significantly enhance the influence of uncertain parameters.