Two kinds of magnesium-based compounds Mg9Si5 and Mg4Si3Al have been prepared under high pressure and high temperature (HPHT) conditions of 5 GPa at 900-1100 °C. Single crystal study revealed that Mg9Si5 crystallizes in space group P6(3) (No. 173) with the lattice parameters a = 12.411(1) Å, c = 12.345(1) Å, and Z = 6. The structure can be derived from the high pressure form Mg2Si with the anticotunnite structure; excess Si atoms of Mg9Si5 form Si-Si pairs in the prismatic cotunnite columns running along the c axis. Mg4Si3Al is obtained by a rapid cooling of a ternary mixture Mg:Al:Si = 1:1:1 from ~800 °C to room temperature under a pressure of 5 GPa. The compound crystallizes in space group P4/ncc (No. 130) with the lattice parameters a = 6.7225(5) Å, c = 13.5150(9) Å, and Z = 4. The structure consists of an alternate stacking of [AlSi2] layers having a Cairo pattern and [Mg4Si] antitetragonal prismatic layers. It can be viewed as composed of hexa-Si-capped tetragonal prismatic cages Mg8Si6 with an Al atom at the center of each cage, Al@Mg8Si6. The compound shows superconductivity with a transition temperature Tc = 5.2 K. The formation regions of the two kinds of new magnesium-based compounds have been proposed.