A quartz glass crucible for use in pulling up a silicon single crystal, wherein it has, at least in the curved portion thereof, a three-layer structure comprising a transparent inner layer being composed of a synthetic quartz glass and having a low Al concentration, a transparent or nontransparent intermediate layer being composed of a natural quartz glass or a mixture of natural and synthetic quartz glasses and having a high Al concentration, and a nontransparent outer layer being composed of a natural quartz glass and having an Al concentration higher than that of the intermediate layer. The quartz glass crucible is reduced in the deformation of the transparent inner layer, and allows the suppression of the change in the amount of dissolution of the quartz glass crucible associated with the pull-up of a single crystal and the achievement of the uniform oxygen concentration in the longitudinal direction of a single crystal.