Let A=( 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 A is called a chain diagonally dominant matrix. the concept was extended to generalized α-chain diagonally dominant matrix，and the concept generalized α-chain diagonally dominant matrix was applied to obtain some new criteria condition for a matrix to be a nonsingular H-matrix. The results obtained improve the known corresponding results．Finally, a numerical example was given for illustrating advantage of results．