Based on the density functional theory with hybrid functional approach, we calculated the structural, electronic, and the optical properties of Cu₂MgSn(S_1-xSe_x)₄ (CMTSSe)，an potential photovoltaic material for thin film solar cells. The calculation reveals a phase transition from kesterite to stannite structure when Zn atoms are substituted by Mg atoms. In particular, the S-to-Se ratio can determine the energy splitting between the electronic states at the top of the valence band. The band gaps of CMTSSe can be tuned in the ranges of 1.01—1.58 eV. Calculated optical properties and tunable band gaps make them beneficial for achieving band-gap-graded solar cells.