The invention relates to a process for manufacturing a part, comprising the formation of successive solid metal layers (201 . . . 20n) that are stacked on one another, each layer describing a pattern defined from a numerical model (M)), each layer being formed by depositing a metal (25), referred to as filling metal, the filling metal being subjected to an input of energy so as to melt and form said layer by solidifying, in which process the filling metal is provided in the form of a powder (25), the exposure of which to an energy beam (32) results in melting followed by solidification such that a solid layer (201 . . . 20n) is formed, the process being characterized in that the filling metal (25) is an aluminum alloy comprising at least the following alloying elements: −2 to 10% by weight of Cr; −0 to 5% by weight, preferably 0.5 to 5% by weight, of Zr. The invention also relates to a part obtained by this process. The alloy used in the additive manufacturing process according to the invention makes it possible to obtain parts having remarkable mechanical properties, while obtaining a process that has an advantageous output.