As a special class of matrix in the mathematical and engineering applications, H-matrix also finds its important application in the fields of numerical algebra, mathematical physics, control theory, etc. Based on the properties of α-chain diagonally dominant, sufficient conditions for the discrimination of the non-singular H-matrix has thus been obtained by constructing the positive diagonal matrix and the index set of partition matrix, and by adopting such techniques as the weighted mean inequality and inequality zooming. Finally, corresponding numerical examples are presented to verify the validity of the determination method.