Abstract: In this paper, according to the concepts of block diagonal dominance and generalize diagonal dominance, a new simple criterion for nonsingular block generalize diagonal dominant matrices (i.e. block H-matrices) are obtained by making use of the norm of submatrices of a given matrix only. Advantages are illustrated by numerical examples. And a necessary condition for nonsingular block Hmatrices is also presented. These results generalize the corresponding results in this area, and make a nodest contribution to this area.