AN important clue to the nature of soft gamma-ray repeaters (SGRs), which emit recurrent bursts of gamma-rays, has been provided by the association of two of the three known SGRs with supernova remnants(1,2) (SNRs). Here we present radio images of the nonthermal radio nebula G10.0-0.3, a supernova remnant which has been associated previously(2) with SGR1806-20 (refs 3, 4). Our images show that the nebula is a plerion (that is, the radio emission is synchrotron radiation powered by a central pulsar), as revealed by the observation of a hierarchy of nested shells and a bright central peak. The recent detection(5) of an X-ray point source coincident with the radio peak and of a hard X-ray burst(5,6) from G10.0-0.3 confirms the SGR-SNR association. We propose that SGR1806-20 is an isolated pulsar that emits both steady and impulsive winds of relativistic particles, which together power the nebula. We suggest that the offset from the centres of the SNRs observed for both this object and SGR0526-66 (ref. 1), requiring high velocities of the pulsars, provides a clue to their formation mechanism.