We report zero field chain-site 63 Cu NQR studies of the low-lying magnetic excitations of CuO zigzag double chains in low-T c and non-superconducting YBa 2 (Cu 1− x Zn x ) 4 O 8 , YBa 2 (Cu 1− x Ni x ) 4 O 8 and Y 1− x Pr x Ba 2 Cu 4 O 8 . For the non-superconducting YBa 2 (Cu 1− x Zn x ) 4 O 8 with x=0.03, we observed a non-vanishing behavior of a 63 Cu nuclear spin-lattice relaxation rate divided by temperature 1/T 1 T at low temperatures, that is, the absence of an energy gap in a magnetic excitation spectrum. The gapless magnetic excitation spectrum of the zigzag chains is characteristic of a quasi-one-dimensional Tomonaga-Luttinger liquid. The Zn-, Ni- and Pr-induced stretched exponential 63 Cu nuclear spin-lattice relaxation times suggest that the Zn-induced edge state has different magnetic correlation from Ni and Pr impurities.