In this paper, polynomial-based projection type and modified projection-type methods for approximating the solution of Hammerstein integral equations with a kernel of Green’s function type are proposed. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and those of superconvergence of the iterated modified projection-type methods are analyzed. A numerical example is given to illustrate the theoretical estimates.