The aluminides CePd2Al2, CePd3Al3, and CePd4Al4 were synthesized and their properties studied by X-ray diffraction, magnetic, heat capacity, and electrical transport measurements. The crystal structures of CePd2Al2 and CePd4Al4 were determined and refined from the single-crystal X-ray diffraction data, while that of CePd3Al3 was designed by the trial-and-error method on the basis of crystal chemistry considerations and refined by the Rietveld method from the X-ray powder diffraction data. All three compounds were found to crystallize in the tetragonal space group P4/nmm with Z = 2. The lattice parameters of CePd2Al2 are a = 4.3974(9) Å and c = 9.871(4) Å. Those of CePd3Al3 are a = 4.3045(7) Å and c = 13.4426(18) Å, while those of CePd4Al4 are a = 4.325(2) Å and c = 16.230(5) Å. The structures represent a new homologous series built of structural units of the CaBe2Ge2- and CsCl-type. The three compounds were established to order antiferromagnetically at 2.5(1) K, 3.5(1) K, and 2.6(1) K for CePd2Al2, CePd3Al3, and CePd4Al4, respectively. All of them are Kondo lattices with the characteristic energy scale of 3-7 K.