In this paper, the first-principles calculations have been performed to study the electronic and magnetic properties of the bulk and (001) surface of Mn 2 CoSn. The bulk Mn 2 CoSn Heusler alloy is found to be a half-metallic ferrimagnet with a total magnetic moment of 3.0μ B per formula unit at the equilibrium lattice constant of 5.85Ǻ. The full-Heusler alloy displays a Slater-Pauling demeanor and the total magnetic moment (M tot ) with the total number of valence electrons (Z tot ) complying the rule Mtot=(Ztot-24). Investigating the electronic density of states, we discover that the half-metallicity confirmed in the bulk Mn 2 CoSn is destroyed at both the Mn(2)Sn- and Mn(1)Co-terminated (001) surfaces. Moreover, we find the atomic magnetic moments at the Mn(2)Sn-terminated (001) surface are increased compared to those of the bulk Mn 2 CoSn, while they increase at the Mn(1)Co-terminated (001) surface. Interestingly, the spin state of Mn(1) atom is turned from low-spin state to high-spin state at the Mn(1)Co-terminated (001) surface, which makes Mn 2 CoSn full-Heusler alloy a promising candidate for spintronic applications.