Additive manufacturing is an established technique in much of industry for manufacturing complex structures from polymer and metal materials. The additive manufacturing of glass materials is a very young process, which is based on through various approaches. For example, such processes are based on a glass powder bed or the layer-by-layer deposition of viscous glass from a crucible. In the Laser Glass Deposition process (LGD), a fused silica glass fiber (0.43 mm) is additively deposited onto a fused silica substrate by CO2 laser irradiation. In order to form structural components from complex contours, or solids, experimental investigations on the printing of homogeneous layers were carried out in this paper. The main focus of the investigations is the influence of the laser power, the printing speed and the line spacing of single tracks and single layers on the deposition morphology. The results were used to realize multilayer complex structures with more than 300 layers.