Abstract: Suppose A is an n by n complex matrix, whether a H-matrix is of important in many application fields is discussed in this paper. Many concept of diagonal dominance of matrices are special cases of H-matrices. The concept of local double α-diagonally dominant matrix is introduced. The new matrix class contains the strictly diagonally dominant matrix, connect diagonally dominant matrix and the matrices. A sufficient condition and an equivalent condition of H-matrices are obtained.