Abstract: In this paper, we first apply properties of irreducible matrices to study nonsingular H-matrices, then conditions for irreducible matrices to be nonsingular H-matrices are obtained. Applying the properties of non-zero elements chain matrices, conditions for them to be nonsingular H-matrices are also obtained. Results obtained do not require that matrices should be diagonal dominant, and are applicable to more matrices. These results are sufficient conditions of nonsingular H-matrices.