In this paper we give a complete analysis of the convergence acceleration method for collocation solutions of Volterra nonlinear integro-differential equations with smooth kernels. It will be shown that when continuous piecewise polynomials of degree m are used and collocation is based on the Lobatto points, the first derivative of this collocation approximation admits, at the knots, an error expansion in even powers of the step-size h, beginning with a term in h2m, On the basis of this expansion we show that when a correction procedure is applied to this collocation approximation for k times: the global accurary of the corresponding corrected approximation will be increased to O(h2m(k+1).