The half-metallic nature with 100% spin-polarization at the surface needs to be conserved to implement the Heusler alloys in spintronic devices. Therefore, we studied the electronic and magnetic properties in bulk and (100), (111)-surfaces of the Co2ScSb Heusler alloy. We performed ab-initio calculations utilizing the GGA and GGA + U approximations. The Co2ScSb Heusler alloy is found to be stable in the ferromagnetic state with an optimized lattice parameter of 6.19 Å. From elastic constant calculations, the alloy considered is mechanically stable with ductile character. The real phonon frequency in whole Brillouin zone confirms the dynamical stability of Co2ScSb alloy. It was found that the half-metallic nature preserved by both approximations and GGA + U gives a larger energy band gap of 0.65 eV and spin-flip gap of 0.10 eV for bulk Co2ScSb alloy. From the investigated layer-density of states, we observed the half-metallicity of 0.13 and 0.06 eV with 100% spin-polarization in ScSb (100) and Sc (111)-surfaces respectively. However, the half-metallic nature is destroyed in CoCo (100), Co (111) and Sb (111)-surfaces because of the surface states presented at the Fermi level. We found that the atomic moments of the S9 layer for five terminations are precisely close to the corresponding bulk values. This work proves that the GGA + U approximation is an appropriate technique to find the half-metallic character in thin-film Heusler alloys.