To address the problem of multiple working conditions and complex requirements in magnetorheological fluid (MRF) mounts, a high-precision damping characteristic optimization method is explored. Based on the parallel plate model, the equation of fluid motion in the inertial channel was established according to the Navier–Stokes equation, and the MRF mount damping characteristics were analyzed. Considering the fluid model to be suitable in the steady-state, the model was experimentally verified, and the extended equation was fitted. Multi-objective optimization design was carried out by considering the large damping force and adjustable coefficient as the optimization goal and external geometric dimensions as variables. According to results, under the radial-channel MRF mount structure, the magnet core depth has the least influence on the damping force; furthermore, the damping performance can be quickly improved by changing the height of the inertial channel. The addition of the extended equations further improved the accuracy of the fluid model. The multi-objective optimization design can improve the strength and uniformity of the flux density of the MRF mount damping gap. After optimization, the damping force is increased by 44.64%; moreover, when the current is increased from 1.5 to 1.8 A, the controllable force increases by only 2.26%, and the damping performance is fully exerted.