We present radio observations of a region in the vicinity of the young pulsar PSR B1853+01 in the supernova remnant W44. The pulsar is located at the apex of an extended feature with cometary morphology. We argue on the basis of its morphology and its spectral index and polarization properties that this is a synchrotron nebula produced by the spin-down energy of the pulsar. The geometry and physical parameters of this pulsar-powered nebula and W44 are used to derive three different measures of the pulsar's transverse velocity. A range of estimates between 315 and 470 km s-1 is derived, which results in a typical value of 375 km s-1. The observed synchrotron spectrum from radio to X-ray wavelengths is used to put constraints on the energetics of the nebula and to derive the parameters of the pulsar wind.