From a series of simultaneous 8.4 and 2.3 GHz VLBI observations of the quasar 4C 39.25 phase referenced to the radio source 0920+390, carried out in 1990-1992, we have measured the proper motion of component b in 4C 39.25: mu(sub alpha) = 90 +/- 43 (mu)as/yr, mu(sub beta) = 7 +/- 68 (mu)as/yr, where the quoted uncertainties account for the contribution of the statistical standard deviation and the errors assumed for the parameters related to the geometry of the interferometric array, the atmosphere, and the source structure. This proper motion is consistent with earlier interpretations of VLBI hybrid mapping results, which showed an internal motion of this component with respect to other structural components. Our differential astrometry analyses show component b to be the one in motion. Our results thus further constrain models of this quasar.