We have measured the proper motion of the candidate optical counterpart of the old, nearby pulsar PSR B1929+10, using a set of HST/STIS images collected in 2001, 7.2 years after the epoch of the original FOC detection (Pavlov et al. 1996). The yearly displacement, mu=107.3+/-1 mas/yr along a position angle of 64.6+/-0.6 deg, is fully consistent with the most recent VLBA radio measurement. This result provides a robust confirmation of the identification of PSR B1929+10 in the optical band.