To prevent excessive displacement of friction pendulum isolators under pulse-type ground motions and further reduce structural seismic responses, an inerter system is integrated with friction pendulum isolators to formulate the nonlinear equations of motion for friction pendulum inerter-isolated structures. Using MATLAB, the seismic response of a single-degree-of-freedom structure under near-fault earthquakes is computed. The maximum displacement of the isolation layer of the friction pendulum inerter-isolated system is compared to the maximum absolute acceleration of the superstructure to investigate its isolation performance. Results demonstrate that the series-parallel type I and type II friction pendulum inerter-isolated systems can effectively mitigate dynamic responses under near-fault ground motions and provide superior isolation under ground motions with rupture forward directivity effects. Larger equivalent damping ratios yield more notable vibration reduction. For equal damping ratios, the series-parallel type I inerter system exhibits fuller hysteresis loops and more effectively constrains isolation layer displacement exceedance, demonstrating enhanced isolation efficacy.