Let [WTHX]A[WTBZ]=([WTBX]aij)∈Cn×n, if there exists α∈(0,1) which can make |aii|≥Rαi(A)S1-αi(A)  be right for i∈N={1,2,…,n}, then [WTHX]A[WTBZ] is called an Ostrowski diagonally dominant matrix. We extended the concept to generalized Ostrowski diagonally dominant matrix，and obtained a new criteria conditions for a matrix to be a nonsingular [WTHX]H[WTBZ]-matrix. The theory of Ostrowski diagonally dominant matrix and nonsingular [WTHX]H[WTBZ]-matrix was improved and completed. These conclusions provide strong basis for the research of relative fields, such as computational mathematics, matrix theory, control theory, mathematical economics, etc.