Whether the retro-aldol reaction observed in the treatment of sugar molecules with hot compressed water occurs via an ionic or a radical reaction remains an open question. Conventionally, the retro-aldol reaction is a known ionic reaction. However, recent experiments performed under hydrothermal conditions have shown that the retro-aldol reaction occurs via a radical reaction. In this work, glyceraldehyde, the simplest sugar to undergo retro-aldol reaction, is used to clearly demonstrate that the retro-aldol reaction of glyceraldehyde under hydrothermal conditions is a radical reaction. Glyceraldehyde was dissolved in deionized water and then heated to 350-450 degrees C at a fixed pressure of 25 MPa in a continuous reactor. The reaction rate of glyceraldehyde followed Arrhenius's Law, irrespective of subcritical or supercritical temperatures. The reaction network of glyceraldehyde was also developed and each reaction rate was determined.