Using the Very Large Array and the Pie Town antenna, we have measured the position of the radio pulsar B1951+32 relative to nearby background radio sources at four epochs between 1989 and 2000. These data show a clear motion for the pulsar of 25 ± 4 milliarcsec yr −1 at a position angle 252 • ± 7 • (north through east), corresponding to a transverse velocity 240 ± 40 km s −1 for a distance to the source of 2 kpc. The measured direction of motion confirms that the pulsar is moving away from the center of its associated supernova remnant, the first time that such a result has been demonstrated. Independent of assumptions made about the pulsar birth-place, we show that the measured proper motion implies an age for the pulsar of 64 ± 18 kyr, somewhat less than its characteristic age of 107 kyr. This discrepancy can be explained if the initial spin period of the pulsar was P 0 = 27 ± 6 ms.