In this paper, Galerkin method is applied to approximate the solution of Volterra integral equations of second kind with a smooth kernel, using piecewise polynomial bases. We prove that the approximate solutions of the Galerkin method converge to the exact solution with the order (Formula presented.) whereas the iterated Galerkin solutions converge with the order (Formula presented.) in infinity norm, where h is the norm of the partition and r is the smoothness of the kernel. We also consider the multi-Galerkin method and its iterated version, and we prove that the iterated multi-Galerkin solution converges with the order (Formula presented.) in infinity norm. Numerical examples are given to illustrate the theoretical results. © 2017 Korean Society for Computational and Applied Mathematics