To attenuate the low-frequency vibration transmitted to the driver, a nonlinear seat suspension with high-static-low-dynamic stiffness is designed. First, the force and stiffness characteristics are derived. The nonlinear suspension can achieve the quasi-zero stiffness at the static equilibrium position when the structural parameters are properly designed. Then, a car-seat-human coupled model which consists of a quarter car model, a seat suspension, and a 4 degree-of-freedom human model is established to predict the biodynamic response of the driver. Finally, the isolation performance of the high-static-low-dynamic stiffness seat suspension under two typical road excitations is evaluated separately based on the numerical method. The effects of stiffness ratio, damping ratio, and vehicle speed on the ride comfort are investigated. The results showed that the nonlinear seat suspension outperforms the equivalent linear counterpart and can achieve the best ride comfort when the quasi-zero stiffness condition is satisfied.