Controlled propagation speed of individual magnetic domains in metal channels at the room temperature is obtained via the non-volatile field effect associated with the switchable polarization of P(VDF-TrFE) (polyvinylidene fluoride-trifluoroethylene) ferroelectric polymer. Polarization domains directly written using conducting atomic force microscope probe locally accelerate/decelerate the magnetic domains in the 0.6nm thick Co film. The change of the magnetic domain wall velocity is consistent with the magnetic anisotropy energy modulation through the polarization upward/downward orientation. Excellent retention is observed. The demonstrated local non-destructive and reversible change of magnetic properties via rewritable patterning of ferroelectric domains could be attractive for exploring the ultimate limit of miniaturization in devices based on ferromagnetic/ferroelectric bilayers. (C) 2015 AIP Publishing LLC.