The construction of a lunar base and habitation on the Moon has always been on researchers’ minds. Building materials used in in situ lunar resources are of great significance for saving expensive space freight. In this study, a new type of lunar soil simulant named Beihang (BH)-1 was developed. The chemical mineral composition and microstructure of BH-1 closely resemble those of real lunar soil, as verified by X-ray fluorescence spectroscopy (XRF), X-ray diffraction (XRD), scanning electron microscopy (SEM), and reflectance spectra. This research also synthesized a geopolymer based on BH-1 cured at simulated lunar atmospheric conditions. We also investigated the effect of supplementing aluminum (Al) sources on the enhancement of geopolymer strength based on BH-1. The rheological behavior of alkali-activated BH-1 pastes was determined for workability. XRF, XRD, Fourier transform infrared spectroscopy, SEM coupled with energy dispersive spectroscopy, and 27Al magic angle spinning-nuclear magnetic resonance were used to characterize resulting geopolymers. Rheological test findings showed that the rheology of BH-1 pastes fits the Herschel–Bulkley model, and they behaved like a shear-thinning fluid. The results showed that the 28-day compressive strength of the BH-1 geopolymer was improved by up to 100.8%. Meanwhile, the weight of additives required to produce per unit strength decreased, significantly reducing the mass of materials transported from the Earth for the construction of lunar infrastructure and saving space transportation costs. Microscopic analyses showed that the mechanism to improve the mechanical properties of the BH-1 geopolymer by adding an additional Al source enhances the replacement of silicon atoms by Al atoms in the silicon–oxygen group and generates a more complete and dense amorphous gel structure.