Recent discovery of colossal magnetoresistance (CMR) phenomena in perovskite manganese oxides has evoked great interest for its physical peculiarity and the possible industrial application. Besides manganese oxides, CMR phenomena is also observed in $Tl_2Mn_2O_7$ with pyrochlore structure and in Cr-based chalcogenide with spinel structure. In this paper, we have studied electronic structures of Cr-based chalcogenide spindles $Fe_{1-x}Cu_xCr_2S_4$ at x=0.0, 0.5, 1.0 using the linearized muffin-tin orbital (LMTO) band method within the local density approximation (LDA). The characteristic resistivity for x=0.0, 0.5 could be explained qualitatively in terms of the half-metalic electronic structure and the Jahn-Teller effect. Especially, the half-metallic nature appearing in the metallic temperature regime is well descibed by the proposed conduction model for x=0.0, 0.5, 1.0. We have suggested, based on the conduction model, that the CMR phenomena observed in these compounds are closely correlated with the obtained half-metallic electronic structure.