We study the Fredholm integro-differential equation Dσ(x) + ∫k(x - y)σ(y)dy = g(x) by the wavelet method. Here σ(x) is the unknown function to be found, k(y) is a convolution kernel and g(x) is a given function. Following the idea in [7], the equation is discretized with respect to two different wavelet bases. We then have two different linear systems. One of them is a Toeplitz-Hankel system of the form (H + T)x = b where T is a Toeplitz matrix and H is a Hankel matrix. The other one is a system (B + C)y = d with condition number κ = O(1) after a diagonal scaling. By using the preconditioned conjugate gradient (PCG) method with the fast wavelet transform (FWT) and the fast iterative Toeplitz solver, we can solve the systems in O(nlogn) operations.