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Aims. The Herschel-ATLAS survey (H-ATLAS) will be the largest area survey tobe undertaken by the Herschel Space Observatory. It will cover 550 sq. deg. ofextragalactic sky at wavelengths of 100, 160, 250, 350 and 500 microns whencompleted, reaching flux limits (5 sigma) from 32 to 145mJy. We here presentgalaxy number counts obtained for SPIRE observations of the first ~14 sq. deg.observed at 250, 350 and 500 microns. Methods. Number counts are a fundamentaltool in constraining models of galaxy evolution. We use source catalogsextracted from the H-ATLAS maps as the basis for such an analysis. Correctionfactors for completeness and flux boosting are derived by applying ourextraction method to model catalogs and then applied to the raw observationalcounts. Results. We find a steep rise in the number counts at flux levels of100-200mJy in all three SPIRE bands, consistent with results from BLAST. Thecounts are compared to a range of galaxy evolution models. None of the currentmodels is an ideal fit to the data but all ascribe the steep rise to apopulation of luminous, rapidly evolving dusty galaxies at moderate to highredshift.

The Herschel-ATLAS: Extragalactic Number Counts from 250 to 500 Microns