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We have explored a spontaneous domain wall motion in ferromagnetic nanowire at zero external magnetic field by means of micromagnetic simulation. Very interestingly, even with no external magnetic field, a spontaneous domain wall motion is observed with a speed about few tens of m/s, which is significant and not negligible in analysis of the domain wall dynamics on nanowires. The spontaneous zero-field wall motion is explained based on the minimization condition of the magnetostatic energy, preferring to have a wire magnetically saturated. Average speed of the spontaneous wall motion is found to increase as the wire thickness increases.