To suppress vertical flexural vibration of a railway vehicle car body, a new passive control method by mounting dampers on the longitudinal beams of the car body underframe is proposed. The method is firstly studied by an Euler-Bernoulli beam model using Green’s functions, then it is further verified by a nonlinear dynamic model of the vehicle. Results show that the car body flexural vibration can be noticeably reduced by this method. It is better to mount the damper near the car body centre. The higher damping coefficient of the damper, the more effective in decreasing the car body first vertical bending vibration. The higher the rigidity of the damper bracket and rubber bush, the better performance of the damper. It is found that when mounting six dampers at proper positions, the damping coefficient of each damper is 1.33×107 N·s/m, even if the first vertical bending frequency of the studied car body is only 7.2 Hz, a very good ride quality will be achieved when the vehicle runs at 250 km/h.