In this article, a Jacobi spectral Galerkin method is developed for weakly singular Volterra integral equations of the second kind. To obtain the superconvergence results, we transform the domain of integration of Volterra integral equation to the standard interval [ - 1 , 1 ] using variable transformation and function transformation. We obtain the convergence rates both in infinity and weighted L2-norm. We prove that the Jacobi spectral iterated Galerkin method shows improvement over the Jacobi spectral Galerkin method. We improve these results further by considering the Jacobi spectral iterated multi-Galerkin method. Theoretical results are justified by the numerical results. © 2019, Springer Nature Switzerland AG.