In previously reported researches on bound state in the continuum (BIC) waveguides, almost all of them are demonstrated with top-down fabrication procedures, leading to inconvenience for post-manipulation and size tuning. Nanofibers with circular cross sections are the fundamental components to transport energy due to their intrinsic advantages of high flexibility and adjustability, which is replaceable and can be readily manipulated over size and position on the substrate. In this work, we explore the possibility of achieving on-chip integration of silica nanofiber onto a silicon-on-insulator platform. By constructing additional leakage channels in coupled nanofiber waveguides, coherently destructive interferences are successfully achieved. The heavy leakage losses from the low-index nanofiber to a high-index silicon substrate are completely eliminated with BIC, and the propagation length of the nanofiber waveguide is significantly improved.