We present a catalogue of high-velocity clouds (HVCs) from the Galactic All Sky Survey (GASS) of southern-sky neutral hydrogen, which has 57 mK sensitivity and 1 km/s velocity resolution and was obtained with the Parkes Telescope. Our catalogue has been derived from the stray-radiation corrected second release of GASS. We describe the data and our method of identifying HVCs and analyse the overall properties of the GASS population. We catalogue a total of 1693 HVCs at declinations < 0 deg, including 1111 positive velocity HVCs and 582 negative velocity HVCs. Our catalogue also includes 295 anomalous velocity clouds (AVCs). The cloud line-widths of our HVC population have a median FWHM of ~19 km/s, which is lower than found in previous surveys. The completeness of our catalogue is above 95% based on comparison with the HIPASS catalogue of HVCs, upon which we improve with an order of magnitude in spectral resolution. We find 758 new HVCs and AVCs with no HIPASS counterpart. The GASS catalogue will shed an unprecedented light on the distribution and kinematic structure of southern-sky HVCs, as well as delve further into the cloud populations that make up the anomalous velocity gas of the Milky Way.