Single crystals of magnesium substituted PdCoO2 have been successfully grown using a metathetical reaction. The crystals show silvery metallic lustre and have a form of habitual polyhedral shape. The maximum size of the grown crystals is about 1.0 x 1.0 x 0.3 mm(3), which is larger than pure PdCoO2 crystals. Polygonal growth steps on the surface and bunchings on the side wall of the crystals are observed. This indicates that the crystals are grown layer by layer. The chemical composition of the crystals inspected by scanning electron microscope-electron probe microanalyzer inductively coupled plasma spectrocopy ICP and Thermo-gravimetry-differential thermal analysis is Pd1.000Co0.982Mg0.018O2.00 This suggests that magnesium ions substitute cobalt ions. Magnetic susceptibilities in a magnetic field of 1 T show the Curie-Weiss type temperature dependence.