The differential cross-sections for elastic scattering of F-17 and O-17 on Pb-208 have been measured at Radioactive Ion Beam Line at Lanzhou (RIBLL). The variation of the logarithms of differential cross-sections with the square of scattering angles shows clearly that there exists a turning point in the range of small scattering angles (6 degrees-20 degrees) for F-17 having exotic structure, while no turning point was observed in the O-17 elastic scattering. The experimental results have been compared with previous data. Systematical analysis on the available data seems to conclude that there is an exotic behavior of elastic scattering differential cross-sections of weakly bound nuclei with halo or skin structure as compared with that of the ordinary nuclei near stable line. Therefore the fact that the turning point of the logarithms of differential cross-sections appears at small angle for weakly bound nuclei could be used as a new probe to investigate the halo and skin phenomenon.