The invention relates to a non-Newtonian fluid lining support structure. The non-Newtonian fluid lining support structure comprises a tunnel primary lining body, a reserved deformation layer formed bya certain space is arranged between the tunnel primary lining body and a tunnel secondary lining body, and a non-Newtonian fluid filling material is placed in the reserved deformation layer; the non-Newtonian fluid filling material comprises a fully-enclosed bag body filled with non-Newtonian fluid inside; a rubber valve is provided with a water injection hole and a pressure relief/grouting hole,a second water injection hole is further formed in the outer side surface, corresponding to the wall rock, of the enclosed bag body, the second water injection hole communicates with a second main water injection pipe embedded in the non-Newtonian fluid of the non-Newtonian fluid filling material, and the second main water injection pipe is connected with arc-shaped sub water injection pipes at intervals. According to the Non-Newtonian fluid lining support structure and a construction method, the problems that stress of a secondary lining steel arc frame is not uniform, and the supporting ability is poor are solved, point force or line force of the wall rock on the secondary lining structure is transformed to surface force, and the using ratio of the secondary structure is improved.