The structural, mechanical, electronic, magnetic, and half-metallic properties of quaternary Heusler compound CoCrScSn are studied using the GGA and GGA + U method based on first-principles calculations. It is found that Type-I structure of CoCrScSn compound is the most stable, and its ground state is ferromagnetic. At the equilibrium lattice constant, the electronic structures obtained by GGA and GGA + U methods indicate that CoCrScSn compound have typical half-metal character. The results of elastic constants and half-metallic robustness show that the mechanical stability and half-metallicity of CoCrScSn can be well-maintained in the range of 6.2–6.9 Å under GGA and 5.7–6.4 Å under GGA + U, respectively. When CoCrScSn compound exhibits half-metallic properties, the total magnetic moment per molecular unit is 4.0 μB, which is in good agreement with the Slater-Pauling rule, and Cr atoms are the main source of molecular magnetic moment. All the aforementioned results indicate that quaternary Heusler compound CoCrScSn would be an ideal candidate in spintronics.