The ternary copper-based chalcogenides Cu(3)MnCh(4) (Ch = S, Se and Te), which have simple cubic (SC) crystal structure and conform to space group with 215 space number, have been investigated by spin-polarised Generalised Gradient Approximation (GGA) in the framework of Density Functional Theory (DFT). First, all systems have been considered in ferromagnetic (FM) and three different type antiferromagnetic (AFM) orders which are A-type (A-AFM), G-type (G-AFM) and C-type (C-AFM) to investigate most stable magnetic phase for each system. The energetically favoured magnetic phase is A-type AFM for Cu3MnS4 and Cu3MnSe4 compounds, while Cu3MnTe4 compound has FM ground state. The electronic band structures of these systems have been investigated, after the well-optimised structural parameters in their stable magnetic phase have been obtained. The calculated spin-polarised electronic band structure of FM Cu3MnTe4 compound exhibits half-metallic behaviour with a band gap in minority spin channel (E-g = 0.99 eV) while metallic band structure is observed for majority spin. The calculated electronic band structures in A-type AFM phase for Cu3MnS4 and Cu3MnSe4 systems show that Cu3MnS4 compound has semiconducting behaviour with a small band gap (E-g = 0.21 eV) whereas Cu3MnSe4 compound has metallic character. The calculated negative formation enthalpies indicate the thermodynamic stability and structural synthesisability of these compounds.