van der Waals (vdW) layered transition-metal chalcogenides are attracting significant attention owing to their fascinating physical properties. This group of materials consists of abundant members with various elements, having a variety of different structures. However, all vdW layered materials studied to date have been limited to crystalline materials, and the physical properties of vdW layered quasicrystals have not yet been reported. Here, we report on the discovery of superconductivity in a vdW layered quasicrystal of Ta1.6Te. The electrical resistivity, magnetic susceptibility, and specific heat of the Ta1.6Te quasicrystal fabricated by reaction sintering, unambiguously validated the occurrence of bulk superconductivity at a transition temperature of ~1 K. This discovery can pioneer new research on assessing the physical properties of vdW layered quasicrystals as well as two-dimensional quasicrystals; moreover, it paves the way toward new frontiers of superconductivity in thermodynamically stable quasicrystals, which has been the predominant challenge facing condensed matter physics since the discovery of quasicrystals almost four decades ago.