A surface modified quartz glass crucible and a process for modifying the crucible includes a layer of a metal oxide on the whole or a part of the inside and/or outside of the crucible, and baking it. At least an inside surface of the crucible is coated with a said metal oxide of magnesium, calcium, strontium or barium. The coated layer of the crucible does not abrade easily and provides a high dislocation free ratio of silicon single crystals pulled by using the crucible.