This paper presents a synthesis method to design a new type of bandpass frequency selective surfaces (FSSs) with multiple transmission zeros (TZs). To briefly show the concept of our synthesis method, a generalized topology of the bandpass FSS based on cascaded slotline sections paralleled with bandpass resonators is first presented to map with an alternative nth-order bandpass filtering network with J-inverters and typical LC parallel resonators. Then, two kinds of composite LC parallel resonators, named as LC-LC and L-LC parallel resonators, are introduced and discussed to replace the typical LC parallel resonators, which can produce TZs at skirts of the passband and increase the out-of-band selectivity. The derivations of equivalent relationships between the composite and typical LC resonators are given. Further, for the exploration of bandpass FSS with multiple out-of-band TZs, the realization of these two discussed composite LC parallel resonators is exhibited by inductive and capacitive strip lines loading on slotline structures. The design curves and guidelines are given and discussed correspondingly. To validate our design concept, two FSS examples, a second-order bandpass FSS with four out-of-band TZs and a third-order one with five out-of-band TZs are synthesized and designed. In final, these two designed bandpass FSS prototypes are fabricated and then measured by the free-space measurement method. The measured results show that the desired stable bandpass filtering performance and independently multiple out-of-band TZs are successfully realized.