In this paper, a class of bandpass frequency selective structures (FSSs) with improved out-of-band rejection is proposed by using stacked slotlines. The proposed FSS consists of a periodic array of slotlines etched in pieces of single-layer printed circuit boards, which are vertically placed along the periodic plane and then stacked together with a certain distance. Due to this special arrangement, slotline resonators are constructed based on the desired propagation modes, thus leading to a stable bandpass filtering response in a wide frequency range. To better understand the operating principle, design procedure of this class of FSSs with uniform slotline unit cells, inductor-loaded uniform slotline unit cells, and stepped-impedance slotline unit cells is presented step by step. In particular, the equivalent transmission line models are established and the even-odd mode analysis method is introduced to intensively analyze the resonant and filtering mechanisms. As two examples, a single-polarized FSS and a dual-polarized one, both based on stepped-impedance slotline unit cells, are designed, fabricated, and measured. Measured results indicate that the proposed FSSs feature miniaturized unit-cell size, wide upper rejection band, and stable frequency filtering response under a large variation of incident angles.