Noncentrosymmetric　hybrid　framework　(HF)　materials　are　an　important　system　in　discovering　new　practical　second-order　nonlinear　optical　materials.　We　calculated　the　second　harmonic　generation　(SHG)　response　of　a　noncentrosymmetric　(NCS)　organic-inorganic　HF　compound,　CuMoO3(p2c)　(p2c　=　pyrazine-2-carboxylate)　to　find　that　it　exhibits　the　largest　SHG　response　among　all　known　NCS　HF　materials　with　one-dimensional　helical　chains.　Further　atom　response　theory　analysis　revealed　that　the　metal　atoms　Cu　and　Mo　contribute　much　more　strongly　than　do　nonmetal　atoms　in　determining　the　strength　of　the　SHG　response,　which　is　a　novel　example　in　nonlinear　optical　materials　known　to　date.