For the bulk and (001) surface of Ti2CoSn Heusler alloy, the electronic and magnetic properties in bulk and the surface effect on the structural, electronic and magnetic properties of the alloy for different terminations of (001) surface have been studied by using first-principles calculations. The spin-gapless semiconductor (SGS) ferromagnetismwith the magnetic moment of 3.00 mu(B)/f.u. is confirmed in the bulk Ti2CoSn alloywith Hg2CuTi-type structure. For two ideal terminations (TiCo, TiSn) and three modified terminations (CoCo*, TiTi*, SnSn*), the density of states (DOS) indicates that all terminations destroy the SGS character. Furthermore, we find that the atomic magnetic moments (AMM) decrease for the most atoms on the outmost three layers due to structural relaxation of these atoms inward. Both the DOS and AMMof the central layer L-9 are similar to the corresponding bulk characters because surface effects fade out at the position of the inner layer, 12 angstrom below the sface. (C) 2016 Elsevier B.V. All rights reserved.