One-dimensional van der Waals (vdWs) heterostructures are celebrated for their exceptional thermal management capabilities, garnering significant research interest. Consequently, our research focused on the one-dimensional vdWs heterojunction comprising carbon nanotube half-wrapped in boron nitride nanotube (BNCNT), specifically their thermal rectification (TR) properties. We employed non-equilibrium molecular dynamics to explore the TR mechanism and assess the impacts of temperature, strain, and coupling strength on heat flux and TR ratio. Our findings reveal that the backward heat flux demonstrates greater atomic vibration instability, as indicated by mean square displacement (MSD), compared to forward heat flux. This instability leads to a higher concentration of localized phonons, thereby diminishing the backward heat flux and enhancing TR. Additionally, we utilized MSD to shed light on the negative differential thermal resistance phenomenon and the influence of stress on forward and backward heat fluxes. Remarkably, TR ratios reached 344% at 3% strain and 400% at -1% strain. Calculations of phonon density of states revealed a competitive mechanism between in-plane and out-of-plane phonons coupling in the inner carbon nanotube and an overlap degree of out-of-plane phonon spectra between the inner carbon nanotube and outer boron nitride nanotube. This accounts for the differing trends in forward and backward heat fluxes as coupling strength χ increases, with TR ratios exceeding 1000% at χ = 7.5. This study provides vital insights for advancing one-dimensional vdWs thermal rectifiers.