Abstract: Firstly, we defined a class of essentially quasi-symmetric non-negative tensors, which encompassed a broader class of tensors covering essentially positive tensors, weakly positive tensors and generalized weakly positive tensors. Secondly, we gave an algorithm for the H-spectral radius of an essentially quasi-symmetric non-negative tensor  by applying the property that the H-eigenvalues of the tensor were invariant under diagonal similarity transformations, and used  numerical examples to  illustrate the effectiveness of the algorithm.

Key words: essentially quasi-symmetric non-negative tensor, H-spectral radius, algorithm