Scissor-like seat suspensions (SL-SSs) with magnetorheological damper (MRD) has been commonly studied and applied successfully in vehicle vibration isolation. However, in most cases, modeling for scissor-like isolation structure is still inaccurate because of overlook on MRD’s layout. In this paper, effect of geometric nonlinearity by MRD’s installation position on the vibration isolation performance of a SL-SS is investigated. A dynamic parametric model of the SL-SS with six assembly types is derived considering geometric nonlinearity based on Lagrange equation. Then, the parameter analysis is performed to estimate magnetorheological damping function in SL-SS. The displacement transmissibility is solved via harmonic balance method, and its effectiveness is validated with numerical results. Finally, comparative study on displacement transmissibility for six assemble types is carried out, and metrics are introduced to access the isolation capabilities of the SL-SS. The results show that the system in type 3 has wider isolation band than other types. And the results also reveal that for type 1, 3 and 6, a minimum isolation frequency may realize, meanwhile, the maximum peak transmissibility also inevitably occurs; for type 5, increasing horizontal distance between installation points of MRD broadens isolation band, but leads to increment of peak transmissibility.