The missing member of the rosiaite family, CoGeTeO , was synthesized by mild ion-exchange reactions and characterized by magnetization and specific heat measurements. It exhibits a successive short- and long-range magnetic ordering at ≈ 45 K and = 15 K, respectively. Based on these measurements, the magnetic - phase diagram was established, showing two antiferromagnetic phases separated by a spin-flop transition. The reason why the pronounced short-range correlation occurs at a temperature nearly three times higher than was found by evaluating the Co-O⋯O-Co exchange interactions using energy-mapping analysis. Although CoGeTeO has a layered structure, its magnetic structure consists of three-dimensional antiferromagnetic lattices made up of rhombic boxes of Co ions. The experimental data obtained at high temperatures agree well with the computational results by treating the Co ions of CoGeTeO as = 3/2 ions, but the heat capacity and magnetization data were obtained at low temperatures by treating the Co ion as a = 1/2 ion.