Density　functional　theory　calculations　have　been　performed　to　investigate　the　linear　and　second-order　nonlinear　optical　(NLO)　properties　of　titanium-based　MIL-125　metal-organic　frameworks　in　crystalline　form,　in　which　the　1,4-benzenedicarboxylate　(BDC)　linkers　are　modified　by　introducing　different　functional　groups　or　by　extending　the　BDC　ligand　to　contain　two　(MIL-126)　and　three　(MIL-127)　benzene　rings.　Our　results　reveal　that　the　functionalization　of　the　BDC　linker　tends　to　increase　the　dielectric　constants　and　the　magnitude　of　birefringence　of　MIL-125,　especially　for　the　aminated　derivatives.　Correspondingly,　the　incorporation　of　a　substituent　group　will　improve　the　phase　matching　performance　of　MIL-125.　As　for　the　second-harmonic　generation　(SHG)　susceptibility,　the　SHG　activity　of　the　pristine　MIL-125　is　comparable　to　KDP,　which　can　be　attributed　mostly　to　the　contributions　of　TiO5(OH)　octahedra.　It　is　noted　that　after　introducing　the　substituent　group　into　the　BDC　linker,　the　organic　part　will　have　a　remarkable　influence　on　the　SHG　intensity.　However,　the　specific　effect　on　the　NLO　response　is　dependent　on　the　type　of　functional　group　incorporated　into　the　BDC　ligand,　and　only　the　inclusion　of　the　amine　group　that　is　strongly　electron-donating　can　obviously　enhance　the　SHG　activity　of　MIL-125.　In　addition,　MIL-126　and　MIL-127　with　longer　aromatic　linking　units　are　not　suitable　to　act　as　NLO　materials　due　to　their　poor　phase　matching　abilities,　but　they　are　promising　candidates　for　the　low　dielectric　constant　materials.　The　present　study　can　provide　theoretical　insights　to　design　new　second　order　NLO　materials　based　on　MIL-125.