A design study was carried out at the German Aerospace Center (DLR) in Bremen, investigating the optimal structural design for a lunar greenhouse module. On account of the volume requirements of a lunar greenhouse and the volume constraints of modern launchers, the study has considered only inflatable and hybrid structures. A literature study was performed on the existing technologies and concepts of fully inflatable and partially inflatable (hybrid) space habitats and structures. Additionally, a review of the lunar environment was carried out and the impact on the lunar greenhouse module structure design was determined. Using system engineering tools, the structural requirements of the greenhouse module were defined. Concepts, such as a cylinder or semi-cylinder, were developed and assessed using an Analytical Hierarchy Process (AHP). A preliminary design of the structure was performed for the selected concept, a semi-cylinder with rigid end-caps and a flexible middle section. For the preliminary design, the gas retention properties as well as the micro-meteoroid and radiation shielding capabilities were designed and thermal and load-bearing properties of the structure were analysed. Additionally, a possible configuration of the greenhouse module interior was presented and interfaces between the rigid and flexible sections of the structure, as well as between the structure and other lunar base structures were discussed. Verification of the preliminary design calculations and the compliance with the requirements was carried out for the thermal and load-bearing structural properties, using the finite element analysis tool MSC Nastran. The final structure design is a semi-cylindrical hybrid structure with rigid end-caps, 20 m in length and with a 3 m radius and with a total mass of 43786 kg. Radiation protection is provided by covering the structure with regolith-filled bags. A total thickness of approximately 2,5 m of regolith needs to be applied to the greenhouse to provide sufficient protection for the astronauts and plants within during the envisioned two year mission lifetime.