A multiresolution wavelet algorithm is developed for the fast solution of electromagnetic scattering problems. A multiscale feature of the spectral domain Green's function is observed in the joint spectral-spatial representation. Owing to the multiscale nature of the electrodynamic Green's function in the spectral domain, wavelet application in the spectral domain (KDWT) is more appropriate in representing the Green's function than the wavelet transform applied in the space domain (SDWT). Using the KDWT, a sparse moment impedance matrix, which is a discretized form of the Green's function, is obtained and a fast multiresolution moment method algorithm is developed in conjunction with the conjugate gradient solver. For a square cylinder the sparsity of the moment method matrix and the resulting time performance are compared with those from the conventional moment method. It is found that the KDWT algorithm leads to a matrix-vector multiplication which scales with an order less than N2.