We report on radio continuum and H i observations of the radio source G328.4+0.2 using the Australia Telescope Compact Array . Our results confirm G328.4+0.2 to be a filled-center nebula with no surrounding shell , showing significant linear polarization and an almost flat spectral index . These results lead us to conclude that G328.4+0.2 is a Crab-like , or “ plerionic ” , supernova remnant ( SNR ) , presumably powered by an unseen central pulsar . H i absorption towards G328.4+0.2 puts a lower limit on its distance of 17.4 \pm 0.9 kpc , making it the largest ( D = 25 pc ) and most luminous ( L _ { R } = 3 \times 10 ^ { 35 } erg s ^ { -1 } ) Crab-like SNR in the Galaxy . We infer G328.4+0.2 to be significantly older than the Crab Nebula , but powered by a pulsar which is fast spinning ( P < 20 ms ) and which has a comparatively low magnetic field ( B < 10 ^ { 12 } G ) . We propose G328.4+0.2 , G74.9+1.2 and N157B as a distinct group of large-diameter , high-luminosity Crab-like SNRs , all powered by fast-spinning low-field pulsars .