A method for producing a part made of composite material includes adding a thermoplastic or thermosetting matrix around a preform of a reinforcing fiber mesh made by filament winding around the spurs or the like of a frame. There is winding in addition to the fibers on one or several reels within the matrix, the axes of the spurs or the like and those of the one or more reels having different orientations, so as to provide the mesh of fibers with a three-dimensional shape.