Let F be a simple graph, and Berge F is a hypergraph if each edge of Berge F is obtained by replacing edges in F with hyperedges. Hypergraph is Berge F-free if it does not contain suphypergraph Berge F. The spectral Turan - problem of linear uniform hypergraphs with special structure based on Aα-tensors is studied, and prove the spectral extreme values of Berge C4-free and linear uniform hypergraphs with girth at least 5 respectively.