The invention discloses a self-adaptive structure for displacement of a tunnel by an active fault sectional mining method. An anti-offset area is arranged at a section, longitudinally crossing the active fault, of the tunnel, and comprises sprayed concrete (1), secondary lining (2) and a filling layer, wherein the filling layer is arranged between the sprayed concrete (1) and the secondary lining(2) and is of a half-coating structure; the filling layer comprises a bottom filling section and side filling sections, the bottom filling section is arranged at the bottom part of the tunnel, and theside filling sections are arranged at the side edges of the tunnel; porous rubber (12) is filled into each side filling section, a plurality of support piers (11) are arranged in the bottom filling section at intervals, the porous rubber (12) is arranged between the adjacent support piers (11), and the porous rubber (12) is of a pre-compressed structure. The invention also discloses an installation method of the self-adaptive structure for displacement of the tunnel by the active fault sectional mining method. The displacement self-adaptive structure provides by the invention provides supportfor the tunnel structure, and is capable of reducing the offsetting quantity of the structure.