A method of producing a quartz glass crucible by arc melting a quartz powder molded product loaded on the inner side of a mold while performing vacuum suction, includes initiating the melting of quartz powder from the rim edge of a quartz powder molded product, subsequently lowering the arc electrode or raising the mold to heat and melt the sections on the downside of the rim edge. The method is preferably carried out such that the inner surface of the crucible is sealed within a time corresponding to 10% of the total arc time starting from the initiation of arc melting, and the seal thickness is 3 mm or less. The quartz glass crucible thus produced is useful for the pulling up of silicon single crystals and has a uniform glass layer with fewer internal bubbles.