The velocity field of the M87 jet from milli-arcsecond (mas) to arcsecond scales is extensively investigated together with new radio images taken by EVN observations. We detected proper motions of components located at between 160 mas from the core and the HST-1 complex for the first time. Newly derived velocity fields exhibits a systematic increase from sub-to-superluminal speed in the upstream of HST-1. If we assume that the observed velocities reflect the bulk flow, we here suggest that the M87 jet may be gradually accelerated through a distance of 10^6 times of the Schwarzschild radius of the supermassive black hole. The acceleration zone is co-spatial with the jet parabolic region, which is interpreted as the collimation zone of the jet (Asada & Nakamura 2012). The acceleration and collimation take place simultaneously, which we suggest a characteristic of magnetohydrodynamic flows. Distribution of the velocity field has a peak at HST-1, which is considered as the site of over-collimation, and shows a deceleration downstream of HST-1 where the jet is conical. Our interpretation of the velocity map in the M87 jet gives a hypothesis in AGNs that the acceleration and collimation zone of relativistic jets extends over the whole scale within the sphere of influence of the supermassive black hole.
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