We describe the reduction of data taken with the PACS instrument on board the Herschel Space Observatory in the Science Demonstration Phase of the Herschel-ATLAS (H-ATLAS) survey, specifically data obtained for a 4 x 4 deg(2) region using Herschel's fast-scan (60 arcsec s(-1)) parallel mode. We describe in detail a pipeline for data reduction using customized procedures within HIPE from data retrieval to the production of science-quality images. We found that the standard procedure for removing cosmic ray glitches also removed parts of bright sources and so implemented an effective two-stage process to minimize these problems. The pronounced 1/f noise is removed from the timelines using 3.4- and 2.5-arcmin boxcar high-pass filters at 100 and 160 mu m. Empirical measurements of the point spread function (PSF) are used to determine the encircled energy fraction as a function of aperture size. For the 100- and 160-mu m bands, the effective PSFs are similar to 9 and similar to 13 arcsec (FWHM), and the 90-per cent encircled energy radii are 13 and 18 arcsec. Astrometric accuracy is good to less than or similar to 2 arcsec. The noise in the final maps is correlated between neighbouring pixels and rather higher than advertised prior to launch. For a pair of cross-scans, the 5 sigma point-source sensitivities are 125-165 mJy for 9-13 arcsec radius apertures at 100 mu m and 150-240 mJy for 13-18 arcsec radius apertures at 160 mu m.