In this work, motivated by the fabrication of an AlSb monolayer, we have focused on the electronic, mechanical and optical properties of AlSb and InSb monolayers with double-layer honeycomb structures, employing the density functional theory approach. The phonon band structure and cohesive energy confirm the stability of the XSb (X = Al and In) monolayers. The mechanical properties reveal that the XSb monolayers have a brittle nature. Using the GGA + SOC (HSE + SOC) functionals, the bandgap of the AlSb monolayer is predicted to be direct, while InSb has a metallic character using both functionals. We find that XSb (X = Al, In) two-dimensional bodies can absorb ultraviolet light. The present findings suggest several applications of AlSb and InSb monolayers in novel optical and electronic usages.