A spider-web-like multi-hole variable cross-section phononic crystal (VCSPC) is proposed, along with a folding method for constructing thin sandwich panels to achieve lightweight and compact structures for low-frequency vibration suppression. The band-gap (BG) characteristics and vibration modes are analyzed using the finite element method (FEM). Both finite element simulation and experimental verification of the frequency response function (FRF) are conducted. The results demonstrate that the spider-web-like configuration, with distributed masses and periodically varying cross-sections, can reduce the opening frequencies of BGs. Compared to the conventional linearly arranged panel, the folding structure exhibits equivalent BGs and attenuations. It is important to note that the proposed folding design significantly reduces the size in the direction of vibration. This type of thin sandwich panel is well-suited for engineering environments with size limitations on vibration reduction structures. The proposed strategy facilitates the use of large-scale phononic crystals (PCs) for low-frequency vibration control through a compact structural design.