In　this　paper　a　nonpolynomial　Jacobi　spectral-collocation　(NJSC)　method　for　the　second　kind　Fredholm　integral　equations　(FIEs)　with　weakly　singular　kernel　|s-t|(-gamma)　is　proposed.　By　dividing　the　integral　interval　symmetrically　into　two　parts　and　applying　the　NJSC　method　symmetrically　to　the　two　weakly　singular　FIEs　respectively,　the　mild　singularities　of　the　interval　endpoints　can　be　captured　and　the　exponential　convergence　can　be　obtained.　A　detailed　L-infinity　convergence　analysis　of　the　numerical　solution　is　derived.　The　NJSC　method　is　then　extended　to　two　dimensional　case　and　similar　exponential　convergence　results　are　obtained　for　low　regular　solutions.　Numerical　examples　are　presented　to　demonstrate　the　efficiency　of　the　proposed　method.