The multiband properties of self-similar fractals can be used to design multiband single-layer frequency selective surfaces (FSS). Combined with Floquet periodic boundary conditions, the moments method is applied to characterize the second-order Y-loop fractal FSS frequency response to different valuses of iterative scaling factor F and lattice as the incidence varies, and then the estimated empirical constant is obtained. Experimental results show good correlation to the calculations, indicating that the resonant frequencies are mainly determined by the iteration factor and the initial unit size,while the lattice impacts the transmission coefficient and bandwidth apparently.