We study the first kind integral equation ∫ k(x - y)σ(y)dy = g(x) by the wavelet method. The integral equation is discretized with respect to two different wavelet bases. We then have two different linear systems. One of them is a Toeplitz system and the other one is a system 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 Fourier transform (FFT), we can solve the systems in O(n log n) operations where n is the size of the systems.