To reduce the underwater noise of ships, gearboxes are usually flexibly installed on the ship’s foundation. A reasonable isolator arrangement can effectively reduce the vibration transmitted from the gears to the foundation. In this paper, a dynamic model of a single-stage vibration-isolated gear system is established based on an impedance synthesis approach. This model is a multiple degrees of freedom, multi-mount, and flexible model that can take into account the local stiffness of the housing and foundation. By studying the influence of installation span, installation offset, and number of isolators on the vibrations of the ship’s foundation, it was determined that reducing isolator span is beneficial to isolation, increasing isolator offset can slightly reduce vibration, increasing the number of isolators does not always increase vibration, and the local stiffness characteristics of the housing and foundation have a greater influence than other factors on the isolation performance.