The work aims to study the influence of the primary suspension of the metro vehicle structures and support stiffness and damping of the track structures about the rail corrugation on the ladder track in the sharp curve, and to put forward the multi-parameter fitting and optimizing methods of minimizing the rail corrugation on the ladder track in the sharp curve at the corresponding section. A corresponding finite element model of the wheelsets-rail system with primary suspension on the ladder track in the sharp curve was constructed based on the theory of frictional self-excited vibration in the wheel-rail system. The characteristics that frictional self-excited vibration of the wheel-rail system occurred on the ladder track in the metro’s sharp curve section was analyzed according to the complex eigenvalue analysis. Based on the finite element model, the parametric analysis was developed about the primary suspension of vehicle structures and support stiffness and damping of track structure. The multi-parameter fitting was carried out about crucial parameters for affecting the unstable vibration by adopting the least square method. In accordance with the fitting equation, the genetic algorithm was adopted for optimization of the crucial parameters. The results show that, on the ladder track with curve radius of 350 m, the frictional self-excited vibration is caused by the saturated creep force between wheel and rail. The unstable vibration occurs at the frequency of 439.02 Hz, which leads to the rail corrugation. The four groups of parameters which have crucial influence are vertical stiffness of fasteners, transverse and longitudinal stiffness of fasteners, vertical damping of fasteners, vertical stiffness of damping materials. When the vertical stiffness of the fastener is 36 MN/m, the transverse and longitudinal stiffness of the fastener is 1.68 MN/m, the vertical damping of the fastener is 2.9 kNs/m, and the vertical stiffness of the damping material is 5.57 MN/m, the possibility of rail corrugation can be effectively suppressed.