  We report on radio continuum and HI 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. HI
absorption towards G328.4+0.2 puts a lower limit on its distance of 17.4 +/-
0.9 kpc, making it the largest (D=25 pc) and most luminous (L_R = 3e35 erg/s)
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<1e12 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.
