Under far-field long-period earthquake, liquid storage tanks are easy to be failure because of large amplitude liquid sloshing. In this paper, nonlinear contact is used to simulate behavior of sliding isolation bearing, nonlinear dynamic equation is used to solve fluid-structure interaction, bilinear material model is used to simulate limiting-device, and ۳-D calculation model of sliding isolation concrete rectangular liquid storage tank (CRLST) with limiting-devices is established. Firstly, artificial far-field long-period earthquake waves are synthesized based on the existing seismic records. Secondly, dynamic responses of sliding isolation CRLST under the action of short-period and far-field long-period earthquakes are studied. Thirdly, effects of bi-directional earthquake and structure size on dynamic responses are investigated. Lastly, displacement control measures are discussed. Results show that far-field long-period earthquakes mainly affect horizontal displacement of structure and liquid sloshing wave height, and sliding isolation has obvious control effect on liquid sloshing wave height. Besides, horizontal displacement of structure and liquid sloshing wave height are increased with increase of seismic dimension and structure size. The reasonable designs of sliding isolation bearing and limiting-device can solve the problem that the maximum horizontal displacement of sliding isolation CRLST may exceed the limit under far-field long-period earthquake.