Positive and negative third-order optical nonlinearities have been investigated in single-stranded DNA wrapped semiconducting single-walled carbon nanotubes. It is found that the redox reactions of hydrogen peroxide can reverse the sign of the third-order nonlinearity. The observation proves that the lowest unoccupied molecular orbital has a lower density of electronic states than that of the highest occupied molecular orbital. A three-energy-level model is used to explain the effect of the redox reactions. Raman spectroscopy has also been used to investigate the interaction between single-walled carbon nanotubes and single-stranded DNA.