63 Cu and 65 Cu NQR line shapes, spin-spin and spin-lattice relaxation rates in a high- T c related Cu oxide, La 4 BaCu 5 O 13+δ , have been measured to clarify the difference between superconducting and non-superconducting Cu oxides from a microscopic view point. Although there are two crystallographically inequivalent Cu sites, only one pair of 63 Cu and 65 Cu NQR frequency spectra was observed. From the detailed study of the Fourier transformed spin-echo signal and that of the envelope decay, we attribute the above fact to an accidental coincidence of the NQR frequencies for these two sites. It is shown that the spin-lattice relaxation is manifested by the magnetic interactions in the measured temperature range of 1.4 K–420 K. The relaxation rate, 1/ 63 T 1 , increases monotonically with increasing temperature, obeying 1/ 63 T 1 = a T + b T 3 above about 80 K, but shows a small swelling at low temperatures, suggesting a magnetic instability.