We present a catalog of high-velocity clouds (HVCs) from the Galactic All Sky Survey (GASS) of southern sky neutral hydrogen, which has 57mK sensitivity and 1 km/s velocity resolution and was obtained with the Parkes Telescope. Our catalog has been derived from the stray-radiation-corrected second release of GASS. We describe the data and our method of identifying HVCs and analyze the overall properties of the GASS population. We catalog a total of 1693 HVCs at declinations <0{deg}, including 1111 positive velocity HVCs and 582 negative velocity HVCs. Our catalog 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 that found in previous surveys. The completeness of our catalog is above 95% based on comparison with the HIPASS catalog of HVCs upon which we improve by an order of magnitude in spectral resolution. We find 758 new HVCs and AVCs with no HIPASS counterpart. The GASS catalog will shed 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.