In this paper, we performed calculations on structural, mechanical, electronic and magnetic properties of ternary and quaternary Heusler Compounds (CoxFe1−x)2CrSn, as well as on their possible half-metallic properties, using the GGA or GGA + U method based on first-principles calculations. We found these compounds are all in the Y1-structure phase, which is the most stable and that their ground states are either ferromagnetics or ferrimagnetics. At the equilibrium lattice constant, the electronic structures obtained by GGA or GGA + U methods indicate that three compounds (Fe2CrSn, CoFeCrSn and Co2CrSn)can exhibit typical or almost half-metal character. For CoFeCrSn compound the total magnetic moment per formula unit is 3.0 μB, which is in good agreement with the Slater–Pauling rule, and Cr atoms are the main source of total magnetic moment. All the aforementioned results indicate that at least one or more of these quaternary Heusler compounds would be an ideal candidate in spintronics. We investigated the Curie temperature TC of these compounds and found them higher than 429 K.