The molecular structure of a series of coumarin derivatives were optimized and their second_order nonlinear optical polarizabilities(β) were calculated by the restricted Hartree_Fock (RHF) ab initio level with the 6_31G basis set in Gamess package. The results include both the distribution of charges in the ground and the excitated state and β under the external field(λ=1064nm). It is revealed that this kind of compounds have fairly large second_order polarizabilities. Moreover, there is close relation between the best structures and the high values of β. So we consider that this series of compounds are worthy of being studied further.