This paper is the second in a series describing the Sydney University Molonglo Sky Survey (SUMSS) being carried out at 843MHz with the Molonglo Observatory Synthesis Telescope (MOST). The survey will consist of ~590 4.3deg. x 4.3deg. mosaic images with 45x45cosec|dec.| resolution, and a source catalogue. In this paper we describe the initial release (version 1.0) of the source catalogue consisting of 107,765 radio sources made by fitting elliptical gaussians in 271 SUMSS mosaics to a limiting peak brightness of 6mJy/beam at dec.<=-50deg. and 10mJy/beam at dec.>-50deg.. The catalogue covers approximately 3500deg^2 of the southern sky with dec.<=-30deg., about 43 per cent of the total survey area. Positions in the catalogue are accurate to within 1-2 for sources with peak brightness A>=20mJy/beam and are always better than 10. The internal flux density scale is accurate to within 3 per cent. Image artefacts have been classified using a decision tree, which correctly identifies and rejects spurious sources in over 96 per cent of cases. Analysis of the catalogue shows that it is highly uniform and is complete to 8mJy at dec.<=-50^deg. and 18mJy at dec.>-50deg.. In this release of the catalogue about 7000 sources are found in the overlap region with the NRAO VLA Sky Survey (NVSS) at 1.4GHz. We calculate a median spectral index of alpha=-0.83 between 1.4GHz and 843MHz. This version of the catalogue will be released via the World Wide Web with future updates as new mosaics are released.