One-dimensional (1D) selenium and tellurium crystalize in helical chainlike structures and thus exhibit fascinating properties. By performing first-principles calculations, we have researched the linear and nonlinear optical (NLO) properties of 1D Se and Te, and find that both systems exhibit pronounced NLO responses. In particular, 1D Se is found to possess a large second-harmonic generation coefficient with the χ value being up to 7 times larger than that of GaN, and is even several times larger than that of the bulk counterpart. On the other hand, 1D Te also produces significant NLO susceptibility χ which exceeds that of bulk GaN by 5 times. Furthermore, 1D Te is shown to possess a prominent linear electro-optic coefficient rxxx(0). In particular, the Te chain exhibits a large shift current response and the maximum is twice as large as the maximal photovoltaic responses obtained from BaTiO3. Therefore, 1D Se and Te may find potential applications in solar energy conversion, electro-optical switches, and so on. Finally, the much stronger NLO effects of 1D Se and Te are attributed to their one-dimensional structures with high anisotropy, strong covalent bonding and lone-pair electrons. These findings will contribute further to experimental studies and the search for excellent materials with large NLO effects.