We present the classification of 717 radio-continuum sources from the Australia Telescope Compact Array (ATCA) Catalogue of the Small Magellanic Cloud (SMC). All 717 sources have been categorised into one of three groups: supernova remnants (SNRs), HII regions and background sources. In total, we name 71 sources as HII regions (or candidates) and 21 sources as SNRs (or candidates). Six sources are named as either HII regions or background sources and two are candidate radio planetary nebulae. One source is coincident with an X-ray binary. We classify 616 objects as background sources and present their statistics.