Weakly　singular　Volterra　integral　equations　of　the　second　kind　typically　have　nonsmooth　solutions　near　the　initial　point　of　the　interval　of　integration,　which　seriously　affects　the　accuracy　of　spectral　methods.　We　present　Jacobi　spectral　-collocation　method　to　solve　two-dimensional　weakly　singular　Volterra　-Hammerstein　integral　equations　based　on　smoothing　transformation　and　implicitly　linear　method.　The　solution　of　the　smoothed　equation　is　much　smoother　than　the　original　one　after　smoothing　transformation　and　the　spectral　method　can　be　used.　For　the　nonlinear　Hammerstein　term,　the　implicitly　linear　method　is　applied　to　simplify　the　calculation　and　improve　the　accuracy.　The　weakly　singular　integral　term　is　discretized　by　Jacobi　Gauss　quadrature　formula　which　can　absorb　the　weakly　singular　kernel　function　into　the　quadrature　weight　function　and　eliminate　the　influence　of　the　weakly　singular　kernel　on　the　method.　Convergence　analysis　in　the　L-infinity-norm　is　carried　out　and　the　exponential　convergence　rate　is　obtained.　Finally,　we　demonstrate　the　efficiency　of　the　proposed　method　by　numerical　examples.