Recently, one-dimensional materials have drawn much attention due to their excellent performance in the field of energy storage and thermal management. As a newly synthesized representative of 1D carbon boron compounds, BC3 nanotube (BC3NT), its thermal conductivity and phonon transport mechanism are urgently required for designing electron-related devices and have been still lacking. Herein, the thermal transport properties of BC3NT are investigated using non-equilibrium molecular dynamic simulations. Compared with the carbon nanotube, the lattice analysis and differential charge density revealed that the much lower thermal conductivity of BC3NT stems from the strong phonon coupling induced by the disorders from atomic mass discrepancy and the polarized covalent bond. Furthermore, the temperature and strain effect of thermal conductivity of BC3NT are explored. Interestingly, it is found that for both CNT and BC3NT, the small tensile strain can enhance the thermal conductivity while the large tensile and compressive strain would impede the phonon transport, indicating that the strain strategy can effectively modulate the thermal conductivity of 1D systems. Our studies not only provide a newly perspective to understand phonon transport of 1D systems and could be helpful to extend phonon coupling mechanism to low-dimensional systems.