The structural configuration and phase stability of quaternary Heusler alloys CoCrScSb, CoCrTiSb and CoCrVSb have been systematically investigated. The results show that type-Ⅰ configuration in the cubic ferromagnetic phase has the lowest total energy, and the CoCrScSb and CoCrVSb exhibit half-metallic behavior under cubic ground state. The hull distance justify that the alloys CoCrScSb and CoCrVSb can be considered to be thermodynamically stable and suitable for experimental synthesis. The tetragonal phase transformation was investigated using the total energy change method. It was found that the deformation of CoCrScSb contributes to the energy reduction, with c/a = 1.25 being at the lowest value of energy. Under tetragonal phase the CoCrScSb exhibits metallic behavior. However, the deformation of the alloys CoCrTiSb and CoCrVSb did not reduce the total energy compared to the cubic phase. Elastic studies indicate that CoCrScSb, CoCrTiSb and CoCrVSb have stable mechanical properties, which provides the possibility for their engineering application.