A single-layer ultra-wideband (UWB) stop-band frequency selective surface (FSS) has several advantages in wireless systems, including a simple design, low debugging complexity, and an appropriate thickness. This study proposes a miniaturized UWB stop-band FSS design. The proposed FSS structure consists of a square-loop and metalized vias that are arranged on a single layer substrate; it has an excellent angle and polarization-independent characteristics. At an incident angle of 60°, the polarization response frequencies of the transverse electric and magnetic modes only shifted by 0.003 f0 and 0.007 f0, respectively. The equivalent circuit models of the square-loop and metallized vias structure are analysed and the accuracy of the calculation is evaluated by comparing the electromagnetic simulation. The 20 × 20 array constitutes an FSS reflector with a unit size of 4.2 mm × 4.2 mm (less than one-twentieth of the wavelength of 3 GHz), which realizes an UWB quasi-constant gain enhancement (in-band flatness is <0.5 dB). Finally, the simulation results were verified through sample processing and measurement; consistent results were obtained. The FSS miniaturization design method proposed in this study could be applied to the design of passband FSS (complementary structure), antennas and filters, among other applications.