Reproducing both the mechanical and biological performance of native blood vessels remains an ongoing challenge in vascular tissue engineering. Additive-lathe printing offers an attractive method of fabricating long tubular constructs as a potential vascular graft for the treatment of cardiovascular diseases. Printing hydrogels onto rotating horizontal mandrels often leads to sagging, resulting in poor and variable mechanical properties. In this study, an additive-lathe printing system with a vertical mandrel to fabricate tubular constructs is presented. Various concentrations of gelatin methacryloyl (gelMA) hydrogel were used to print grafts on the rotating mandrel in a helical pattern. The printing parameters were selected to achieve the bonding of consecutive gelMA filaments to improve the quality of the printed graft. The hydrogel filaments were fused properly under the action of gravity on the vertical mandrel. Thus, the vertical additive-lathe printing system was used to print uniform wall thickness grafts, eliminating the hydrogel sagging problem. Tensile testing performed in both circumferential and longitudinal direction revealed that the anisotropic properties of printed gelMA constructs were similar to those observed in the native blood vessels. In addition, no leakage was detected through the walls of the gelMA grafts during burst pressure measurement. Therefore, the current printing setup could be utilized to print vascular grafts for the treatment of cardiovascular diseases.