The re-weighted regularized conjugate gradient (RRCG) method has been a popular algorithm for magnetic inversion problems. In this work, we show that for a two-dimensional problem with uniform field data, the resulting coefficient matrix to be inverted has a symmetric Block-Toeplitz Toeplitz-Block (BTTB) structure. Taking advantage of the BTTB properties, the storage and computational complexity can be significantly reduced, so that the efficiency of the RRCG method is greatly improved and it is now capable of dealing with much larger system with a modest computing resource. This paper also investigates various numerical inversion schemes including the CG type and multigrid (MG) methods. It has been demonstrated that the MG is an efficient and robust numerical tool for magnetic field inversion. Not only the MG produces a rapid convergence rate, the performance is not sensitive when applying to noisy data. Numerical simulations using synthetic data and real field data are reported to confirm the effectiveness of the MG method.