Mechanical model of finite element of rubber isolation and reticulated shell is established, vibration response of single-layer cylindrical reticulated shell structure installed the rubber isolation bearing under earthquake is investigated by numerical method. The results show that isolation bearing can play a good control effect on vibration of the structure, however, seismic intensity can influence the energy dissipation capacity of isolation bearing, energy dissipation ability increases with the increase of the earthquake intensity in maximum range, under the effect of different seismic wave, the vibration control effect of the isolation structure is different; in addition, the vibration control effect of the isolation structure is the best under the seismic wave of EI Centro.