The wavelet-based multigrid method is presented on the comparative study between the multiresolution anaylsis of wavelet theory and multigrid method. The scaling spaces inwavelet theory serve as the grids in the multigrid method. The wavelet transform transfers the information between two grids. It solves the basic difficulty of the construction of grids and thechoice of the sufficiently good transfer formulae between the fine and coarse grids. The numericalresults show that the novel method is convergent faster and more accurate than the conventionalone. Due to the perfect frame of wavelet theory

the coarse grids and transform operators can beconstructed automatically. So this method can be used as a black-box solver for a wide range ofproblems.