Rubber isolators are widely used in engineering structures, which often exhibit some nonlinearity and uncertainty properties subjected to different environment exciting. In order to study the nonlinear characteristic and uncertainty of a rubber isolator system, the sin-sweep vibration tests with different base exciting level are carried out firstly. Then a single freedom degree mass-spring-damper model is introduced to simplify the rubber isolator system. In the theory model, the spring and the damper are represented by polynomial functions of the relative displacement. The coefficients in the functions are identified by the test data, while the uncertainties of the coefficients are quantified by the principal components analysis (PCA) and Monte Carlo (MC) simulations. The major resonant frequencies and the damping ratios of the isolation system are calculated according to the theory model, the amplitude-frequency nonlinear characteristics are simulated by Runge–Kutta numerical method. The simulation results agree well with the experimental results, which indicate that the nonlinear model and the uncertainty quantifying results are feasible to predict the vibration characteristic and uncertainty of the isolation systems.