We report the synthesis of alumina/stishovite nano-nano composite ceramics through a pressure-induced dissociation in Al2SiO5 at a pressure of 15.6GPa and temperatures of 1300 degrees C-1900 degrees C. Stishovite is a high-pressure polymorph of silica and the hardest known oxide at ambient conditions. The grain size of the composites increases with synthesis temperature from similar to 15 to similar to 750nm. The composite is harder than alumina and the hardness increases with reducing grain size down to similar to 80nm following a Hall-Petch relation. The maximum hardness with grain size of 81nm is 23 +/- 1GPa. A softening with reducing grain size was observed below this grain size down to similar to 15nm, which is known as inverse Hall-Petch behavior. The grain size dependence of the hardness might be explained by a composite model with a softer grain-boundary phase.