The quasi-one-dimensional (quasi-1D) materials serve as an excellent platform to realize ultra-low lattice thermal conductivity for thermoelectric applications, attributed to their reduced dimensionality and weak interchain van der Waals (vdW) interactions. Herein, utilizing first-principles calculations and Boltzmann transport theory, we explore the thermoelectric transport properties of the quasi-1D Bi₄RuI₂. Our calculation results indicate that Bi₄RuI₂ exhibits extraordinarily low intrinsic interchain and intrachain lattice thermal conductivity of 0.349 and 1.851 (0.131 and 0.714) W/mK at 300 (800) K, respectively. The damped thermal transport properties originate from the low phonon group velocity and large lattice anharmonicity due to the heavy component elements, complex crystal structure, avoided-crossing effects, lone-pair electrons, and bonding hierarchy. Notably, the lattice thermal conductivity exhibits pronounced anisotropy, which is obviously smaller along the interchain direction than that along the intrachain direction due to the weaker vdW interactions between the 1D covalent chains. Furthermore, Bi₄RuI₂ achieves high figure-of-merit (ZT) values due to the high power-factor and low lattice thermal conductivity, which reaches maximum values of about 1.59 and 2.54 at 800 K along the interchain and intrachain directions by n-type carrier doping. These findings establish quasi-1D Bi₄RuI₂ as a promising candidate for high-performance low-dimensional thermoelectric materials.