Ab initio calculation of the structural, mechanical, dynamic, thermodynamic, electronic, and optical properties of cubic half-Heusler compound NaScSi have been reported using density functional theory. Generalized gradient approximation has been used as the exchange and correlation potential for investigating these properties. The lattice constant, bulk modulus, the first pressure derivative of bulk modulus, and band gap of NaScSi have been calculated and compared to the previous XScSi (X = Na, Li, Ag, K) studies. The band structure and corresponding density of states have also been determined and analyzed. The elastic properties of the compound, calculated by the strain-stress method, satisfy the mechanical stability conditions for a cubic structure. According to the data obtained from the vibration properties, the compound is also stable dynamically. Additionally, heat capacity, entropy, and free energy of NaScSi have been calculated by using the phonon frequencies. The optical investigation of the compound shows high reflectivity in the UV region of the photon energy.