The unsteady 3-D numerical simulation was done in order to clarify the influence of ignition position on high-speed flame propagation phenomenon along a line vortex. The distance between the vortex center line and the ignition position was changed from D = 0 mm to D = 7 mm, while the vortex diameter was fixed at d = 2 mm. In the 3-D visualization, the shapes of flame and vortex line ware considerably different depending on D. Only when the high-speed flame propagation along the vortex occurred, the helical vortex line (the vortex filament solitons) was observed near the flame top. In the 1-D analysis along the vortex line, the peaks of curvature of the vortex line (the vortex filament solitons) were observed at the locations of large temperature gradient (the flames), and the vortex filament solitons and the flames propagated together along the vortex line. Due to these results, the validity of vortex driving mechanism of high-speed flame propagation phenomenon was reconfirmed. Finally, in the analysis of flame propagation speed, the steady maximum speeds reached about 11-12 m/s in all cases of D. However, the startup time of flame propagation depended on D sensitively, and the earliest startup was obtained at D = 0.8 mm, and not at D = 0 mm. Thus, it was found that the optimum ignition position for rapid startup of flame propagation existed, and such a result was explained by using the vortex driving mechanism.