The differential cross sections of 17F and 17O elastic scattering products on 208Pb have been measured at the Radioactive Ion Beam Line at Lanzhou (RIBLL). Two angular dispersion plots of ln (dσ/dθ) versus θ2 are obtained from the angular distribution of the elastic scattering differential cross sections. The angular dispersion plot exhibits a clear turning point for 17F in the range of small scattering angles 6°–20° due to its exotic structure, but for 17O, the turning point is not observed in the same angular range. The experimental results have been compared with previous data of other groups. Systematical analysis on the available data supports the above conclusion that there is an exotic behaviour of the angular dispersion plot of weakly bound nuclei with halo or skin structure as compared with that of the ordinary nuclei near stable line. Therefore the turning point of the angular dispersion plot appears at small angle for weakly bound nuclei with halo or skin structure, and can be used as a new probe to investigate the halo and skin phenomena of weakly bound nuclei.