Abstract: A simpler and more concrete estimate of the upper bound of ‖A^-1‖_∞ than those in previous papers is given, when A is an H-matrix and the equidiagonal dominant matrix is defined.We prove that if A is an equidiagonal-dominant M-matrix with equidiagonal-dominanceδ|i.e.|a₁₁-||a₁₁|=δ,∀_i),则ρ(A^-1)=‖A^-1‖_x=(A^-1)_ij=1/δ,∀_i, By use of equidiagonal-dominant matrix the upper bound of ‖A^-1‖_x for any H-matrx may be found. Several interesting examples are given to illustrate our theorems.