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Employing first-principle calculations, we investigated the influence of the impurity, Fe atom, on magnetism and electronic structures of Heusler compound Ti₂CoSi, which is a spin gapless semiconductor (SGS). When the impurity, Fe atom, intervened, Ti₂CoSi lost its SGS property. As Ti^A atoms (which locate at (0, 0, 0) site) are completely occupied by Fe, the compound converts to half-metallic ferromagnet (HMF) TiFeCoSi. During this SGS→HMF transition, the total magnetic moment linearly decreases as Fe concentration increases, following the Slate–Pauling rule well. When all Co atoms are substituted by Fe, the compound converts to nonmagnetic semiconductor Fe₂TiSi. During this HMF→nonmagnetic semiconductor transition, when Fe concentration y ranges from y = 0.125 to y = 0.625, the magnetic moment of Fe atom is positive and linearly decreases, while those of impurity Fe and Ti^B (which locate at (0.25, 0.25, 0.25) site) are negative and linearly increase. When the impurity Fe concentration reaches up to y = 1, the magnetic moments of Ti, Fe, and Si return to zero, and the compound is a nonmagnetic semiconductor.