A Legendre-collocation method is proposed to solve the nonlinear
Volterra integral equations of the second kind. We provide a
rigorous error analysis for the proposed method, which indicate that
the numerical errors in $L^2$-norm and $L^\infty$-norm will decay
exponentially provided that the kernel function is sufficiently
smooth. Numerical results are presented, which confirm the
theoretical prediction of the exponential rate of convergence.