Context: .Centaurs reside in a region of the Solar System where many volatile species begin to have significant sublimation rates, and several examples of cometary activity have been observed in this group. The source of activity is not well known for most of the active Centaurs. If the sublimation rate of water is low, the sublimation of other volatiles, such as CO, could drive the presence of a coma. Aims: .The aim of this paper is to study the dust environment of the active Centaur P/2004 A1 (LONEOS), which was observed to have a significant coma and a very long perspective anti-tail (neck-line) at a heliocentric distance of 5.5 AU. Methods: .R-band images taken at the TNG telescope were used as input for an inverse numerical model, meant to derive the physical parameters of dust grains in the coma. Results: .The Centaur showed an asymmetric coma and a neck-line extending at least to 1.5 × 105 km in the solar direction, emitted half an orbit before the observation. The Afrho value measured in a 5'' aperture is 334 ± 15 cm, indicating a significant dust production rate, comparable to that of several short-period comets at much lower heliocentric distances. The emitted grains are larger than 1 cm, and the dust production rate has been around 100 kg s-1 during the last ten years. For Rn = 10 km and a maximun size of the uplifted grain >3 cm, a CO molecular abundance Q > 1030 mol s-1 is required if it is uniform over all the surface.