In a search for unconventional heavy-Fermion compounds with the localized 4f moments distributed quasiperiodically instead of a conventional distribution on a regular, translationally periodic lattice, we have successfully synthesized a stable Ce3Au13Ge4 Tsai-type 1/1 quasicrystalline approximant of the off-stoichiometric composition Ce3+xAu13+yGe4+z (x = 0.17, y = 0.49, z = 1.08) and determined its structural model. The structure is body-centered-cubic (bcc), with space group Im3̅, unit cell parameter a = 14.874(3) Å, and Pearson symbol cI174, and can be described as a bcc packing of partially interpenetrating multishell rhombic triacontahedral clusters. The cerium sublattice, corresponding to the magnetic sublattice, consists of a bcc packing of Ce icosahedra with an additional Ce atom in a partially occupied site (occupation 0.7) at the center of each icosahedron. The measurements of its magnetic properties and the specific heat have demonstrated that it is a regular intermetallic compound with no resemblance to heavy-Fermion systems. The partially occupied Ce2 site in the center of each Ce1 icosahedron, the mixed-occupied Au/Ge ligand sites between the Ce2 and Ce1 atoms, and the random compositional fluctuations due to nonstoichiometry of the investigated Ce3+xAu13+yGe4+z alloy introduce randomness into the Ce magnetic sublattice, which causes a distribution of the indirect-exchange antiferromagnetic interactions between the spins. Together with the geometric frustration of the triangularly distributed Ce moments, this leads to a spin-glass phase below the spin freezing temperature Tf ≈ 0.28 K.