The effect of Co addition on the properties of Ni8-xMn4Ga4Cox(x=0, 0.5, 1, 1.5 and 2) ferromagnetic shape memory alloys are systematically investigated by means of the first–principles calculations within the framework of density functional theory (DFT) using the Viennaabinitiosoftware package (VASP). The formation energy results indicate that the added Co preferentially occupies the Ni sites in Ni2MnGa alloy. With the increase of the Co content, the optimized lattice parameters of the parent phase decreases regularly, whereas the lattice parameteraof the martensite increases andcdecreases, thus leading to a decrease of thec/aratio. The effects of Co addition on phase stability of the paramagnetic and ferromagnetic austenite are displayed. The difference in the magnetic properties in the investigated series can be explained from the electronic density of states analysis. The aim of this paper is to provide theoretical guidance for the development of new promising ferromagnetic shape memory alloys with optimized properties.