The study of the astrophysical S-factor is essential in the analysis of low-temperature stellar radioactive capturing reactions in theoretical frameworks. We investigate the proton capture by 17O using Wood Saxon potential model. We calculated the astrophysical S-factor for 17O(p, γ) 18F reactions at low energy. In the hydrogen-burning process, this reaction plays a role in multiple stages of stellar evolution. Furthermore, it is important in the synthesis of fluorine and oxygen isotopes, which is part of the CNO cycle. At low energis, the empirical size of the cross-section of this reaction is not available. As a result, the reaction rate could be used in theoretical models by extrapolating the astrophysical S-factor to extremely low energy levels and finding the cross-section. Finally, transition strengths on the astrophysical S-factor is calculated and it was found that electric dipole(E1) transition in the 500 keV energy range is dominant. The findings are consistent with empirical data and other theoretical models. Furthermore, the S-factor at zeri energy for the (5/2)+ level was calculated using extrapolation, yielding S(0)= 4.807 keV.b .