A miniaturized dual-stopband frequency selective surface (FSS) is proposed in this paper to shield the sensitive electronic equipment from interference signals with closely spaced frequency bands. The proposed FSS composes of a dielectric layer and two metal strip layers printed on both sides of the dielectric substrate. Different from other dual-band FSSes, the coupling between the double metal strip layers of the proposed FSS is weakened intentionally by using the complementary design of the strip patterns. As a result, the proposed FSS has two independently tunable stopbands which are very closely spaced. The simulated results show that the operating bands of the proposed FSS structure can achieve a frequency ratio as low as 1.16. In addition, the miniaturized design by using the convoluted elements makes the dimension of the unit cell as small as 0.071λ, where λ is the wavelength of the lower resonant frequency in free space. This ensures that the proposed FSS has incident angular stability of up to 60° for both TE and TM polarizations, while keeping at least 24 dB shielding effectiveness at the same time. The prototypes of the proposed FSS are fabricated and tested. Good agreements are achieved between the measurement and simulation, which demonstrates the reliability of the simulation.