Aims: We aim to demonstrate that the Herschel-ATLAS (H-ATLAS) is suitable for a blind and unbiased survey for debris disks by identifying candidate debris disks associated with main sequence stars in the initial science demonstration field of the survey. We show that H-ATLAS reveals a population of far-infrared/sub-mm sources that are associated with stars or star-like objects on the SDSS main-sequence locus. We validate our approach by comparing the properties of the most likely candidate disks to those of the known population. Methods: We use a photometric selection technique to identify main sequence stars in the SDSS DR7 catalogue and a Bayesian Likelihood Ratio method to identify H-ATLAS catalogue sources associated with these main sequence stars. Following this photometric selection we apply distance cuts to identify the most likely candidate debris disks and rule out the presence of contaminating galaxies using UKIDSS LAS K-band images. Results: We identify 78 H-ATLAS sources associated with SDSS point sources on the main-sequence locus, of which two are the most likely debris disk candidates: H-ATLAS J090315.8 and H-ATLAS J090240.2. We show that they are plausible candidates by comparing their properties to the known population of debris disks. Our initial results indicate that bright debris disks are rare, with only 2 candidates identified in a search sample of 851 stars. We also show that H-ATLAS can derive useful upper limits for debris disks associated with Hipparcos stars in the field and outline the future prospects for our debris disk search programme. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.