Taking the Burgers equation as example, an adaptive multilevel interpolation quasi-wavelet collocation method for the solution of partial differential equations is developed. In this method, an adaptive multilevel quasi-wavelet collocation interpolation operator is constructed according to the interpolation wavelet theory, and then the equations can be discreted adaptively in physical space. On the other hand, the extrapolation and precise integration method is helpful for decreasing computation time and improving calculating precision, and it make the selection of time step for integration self-adaptive.