Good cyclability is essential for the potential application of cathode materials. We investigated electrochemical properties of Mg in layered intercalation compound from first-principles using TiS₃ as a model system. The calculations showed exothermic phase transformation upon intercalation of Mg from the electrolyte: the geometry optimization of the structure containing 0.5 Mg showed the shift of layers accompanied by change of Mg coordination from square pyramidal to trigonal prismatic. Further increase of the Mg content leads to break of the S-S bonds in the disulfide ion and conversion of the TiS₃ layers into ribbons. The obtained phase is metastable and can easily and irreversibly decompose to MgS and TiS₂. This means that in order to achieve full theoretical capacity of TiS₃ this decomposition has to be suppressed. A very low migration barrier of 0.292-0.698 eV (depending on the Mg content) was found in the [010] direction, which is much lower than the value of analogues, such as layered and spinel TiS₂. This finding reveals the potential of TiS₃ to become Mg cathode with superior performance compared to similar analogues.