This　work　is　to　provide　spectral　and　pseudo-spectral　Jacobi-Galerkin　approaches　for　the　second　kind　Volterra　integral　equation.　The　Gauss-Legendre　quadrature　formula　is　used　to　approximate　the　integral　operator　and　the　inner　product　based　on　the　Jacobi　weight　is　implemented　in　the　weak　formulation　in　the　numerical　implementation.　For　some　spectral　and　pseudo-spectral　Jacobi-Galerkin　methods,　a　rigorous　error　analysis　in　both　the　infinity　and　weighted　norms　is　given　provided　that　both　the　kernel　function　and　the　source　function　are　sufficiently　smooth.　Numerical　experiments　validate　the　theoretical　prediction.　©　Springer　Science+Business　Media,　LLC　2012.