Half-metallic fully compensated ferrimagnets (HM-FCFs) are important spintronic materials due to the high spin polarization and the low magnetic moment. Recently, motivated by the theoretical prediction of HM-FCF of bulk Cr2CoGa, ordered inverse Heusler structural Cr2CoGa thin films were grown by molecular beam epitaxy, and the predicted low magnetic moment and high Curie temperature were also confirmed. Here, in order to compare the electronic and magnetic properties between bulk and thin films for Cr2CoGa, we explore the structural stability, electronic and magnetic properties of Cr2CoGa (001) surface by using first-principles calculations. It is found that the nearly half-metallicity of bulk Cr2CoGa is preserved at the Cr2Ga-terminated (001) surface, and the spin polarization is a little increased compared to the bulk value. However, the Cr1Co-terminated (001) surface destroys the bulk nearly half-metallicity due to the majority-spin surface states at the Fermi level. Cr atomic magnetic moments at both (001) surfaces are greatly increased compared to those in bulk for Cr2CoGa. In addition, we reveal that the Cr2Ga-terminated (001) surface is more stable than the Cr1Co-terminated (001) surface over the whole effective chemical potential. These studies indicate that ordered inverse Heusler structural Cr2CoGa thin films are promising candidates for spintronic applications.