A process for the additive manufacturing of a three-dimensional metal part consists of successively solidifying successively deposited layers of metal powder by melting with a laser beam (120), and defining in each of these successive layers at least one core region (210) and/or at least one shell region. The melting of said core regions (210) is effected with said laser beam (120) so as to form weld beads (211) that have identical widths (L), are mutually parallel and are juxtaposed or spaced apart or overlap over a distance less than X % of their width, and the melting of said shell regions is effected similarly to form weld beads that have identical widths to one another and to the weld beads of the core, are mutually parallel and that overlap over a distance greater than X % of their width, X being greater than 0 and less than 100.