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 0.6 nm 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.