Turán problems of graphs or Hypergraphs are the core issue in the extremal graph theory. In this talk, we consider the spectral version of Turán-type problems over uniform hypergraphs by tensor spectral methods. We first develop two new tools to establish the connection between spectral radius of the adjacency tensor and structural properties of a hypergraph. Then, by these two methods, several spectral versions of Turán-type results on linear k-uniform hypergraphs are obtained. This is the joint work with Yuan Hou, J. Cooper and Guorong Gao.