The mechanical properties, electronic structures and optical properties of CaAlSiN3 were investigated using the first-principles calculations. The elastic constants, bulk moduli, shear moduli, Young's moduli, and Poisson's ratio were obtained. These results indicate that CaAlSiN3 is mechanically stable and a relatively hard material. Moreover, this compound has an indirect band gap of ∼3.4 eV according to its band structure and density of states. The linear photon energy dependent dielectric functions and related optical properties including the refractive index, extinction coefficient, absorption spectrum, reflectivity, and energy loss spectrum were computed and discussed. It is shown that no sizable anisotropy is found in the optical properties of CaAlSiN3. The obtained structural estimation and some other results are in agreement with available experimental and theoretical data. This investigation is not only helpful for better understanding the electronic, mechanical and optical properties of CaAlSiN3, but also will open up the possibility of its use in device applications.