Transmission error is the main excitation source of gear vibration and noise, how to reduce the transmission error has always been the focus of the research on gear dynamics. In this study, a new type of cylindrical spur gear with elastic isolation is developed for the reduction of transmission error. The elastic isolation damping gear includes three parts: the gear body, the elastic isolation layer, and the involute profile body. Dynamic models are established with the elastic isolation damping gear using lumped parameter method. Dynamic characteristics are simulated via spur gear pair examples by the Runge-Kutta algorithm. By comparing the simulation results of three gear models, the dynamic response of the elastic isolation damping gear with sliding friction is illustrated. The influence of different parameters of the elastic isolation layer on the dynamic response for the elastic isolation damping gear model is carried out. The results indicate that the proposed elastic isolation damping gear model is effective in reducing dynamic transmission error, especially for torque fluctuation, high-speed and heavy-duty conditions. Parameter influence analysis guides the design of elastic isolation damping gears with low transmission error.