ABSTRACT Irregular rainfall in the semiarid region of Brazil and in the world exerts a limiting action on agricultural production, in general, including fruit species. Under these conditions, irrigation is the input that keeps the production system both economically and socially viable. This study was carried out from 2012 to 2014, in the municipality of Remígio, Paraíba State, Brazil, aiming at evaluating the production of ‘Morada’ soursop cultivated under rainfed and irrigated conditions, in soil with and without mulch, in two harvests. The treatments were distributed in randomized block design with three replicates in a 2 × 3 × 2 factorial scheme, corresponding to non-irrigated plants (0 mm water depth) and plants irrigated weekly (17.2 mm water depth) in soil without mulching, with cover crop residues, and with a sisal bagasse mulch in the 2012/2013 and 2013/2014 crop years. In the soil without mulching, irrigation increased yield from 5.3 to 34.7 t ha-1 in the first harvest and from 9.4 to 57.7 t ha-1 in the second harvest. The association between irrigation and mulch with sisal residue promoted the highest yield. The use of mulch of sisal residue increased the number and mean mass of fruits, production per plant and yield of ‘Morada’ soursop compared to the soil without mulch and covered by crop residues.