In this paper, we briefly introduce the concept of 3D frequency selective rasorber (FSR) as well as its generalized equivalent circuit model. Based on this understanding, a new kind of 3D FSR based on stacked planar slotline structure is presented. As an example, a prototype 3D FSR is demonstrated to exhibit bandpass filtering response and good absorption performance at both sides of the passband, and it is then fabricated and measured. The measured results show that the minimum insertion loss in the transmission window is about 0.3 dB, and the absorption bandwidths are ranged from 1.6 to 2.3 GHz and from 3.6 to 4.6 GHz, respectively. To further verify the design concept, another design example with wider absorption bands is developed by introducing more lossy resonators.