This work provides a new approach for computing the impedance of a proposed multiband printed fractal antenna for wireless applications. Galerkin’s method is applied to deduce the impedance relationship of the proposed structure and then compute the return loss verses frequency by converting the impedance matrix of the proposed antenna [Z] to the scattering matrix [S]. This model is developed in order to study the impedance of the proposed antenna after adding a metamaterial structure in the antenna substrate. The obtained model is able to determine the resonant frequencies and the return loss of the proposed antenna. The model is also able to define the changes in these values when the dimensions of the proposed structure change. The proposed antenna provides multiband wireless applications in the (1–10) GHz frequency band, and the return loss of the proposed fractal antenna has been improved using negative permittivity and negative permeability metamaterial structure.