Long period ground motion has great influence on long period structures such as large oil tank, high-rise building and long span bridge. In this paper, a long span cable-stayed bridge is taken as an example to study the seismic response of long period structure under long period ground motions and conventional ground motions by using nonlinear dynamic time history method. It is shown that although the peak acceleration of the long period ground motions are no more than half of conventional ground motions, the displacement and force response of the bridge at key points under long period ground motions are much greater than that of conventional ground motions. Constraint cables and fluid viscous dampers are used to reduce in the influence of long period ground motion of the bridge, and the effects of the two countermeasures are also analyzed in this paper. The results show that constraint cables have unstable effect and even negative effect under long period ground motion. While fluid viscous dampers have stable effect under both long period ground motion and conventional ground motion with proper damping parameters.