We report the synthesis, crystal structure, and physical properties of a novel ternary compound, Th2Cu4As5. The material crystallizes in a tetragonal structure with lattice parameters a = 4.0639(3) Å and c = 24.8221(17) Å. Its structure can be described as an alternating stacking of fluorite-type Th2As2 layers with antifluorite-type double-layered Cu4As3 slabs. The measurement of electrical resistivity, magnetic susceptibility, and specific heat reveals that Th2Cu4As5 undergoes bulk superconducting transition at 4.2 K. Additionally, all these physical quantities exhibit anomalies at 48 K, accompanied by a sign change in the Hall coefficient, suggesting a charge-density-wave-like (CDW) phase transition. Drawing from both experimental data and band calculations, we propose that the superconducting and CDW-like phase transitions are, respectively, associated with the Cu4As3 slabs and the As plane in the Th2As2 layers.