There is provided a means which carries out a fire-blast treating effectively upon removing a deteriorated region caused by processing in a process of producing a glass vessel. In a process of producing a glass vessel by fire-blast treating an internal surface 10 of a preform of the glass vessel with a flame from a burner 30 so as to produce the glass vessel, said fire-blast treating is carried out such that a temperature of an outer surface portion of the preform which portion is opposed to the deteriorated region caused by processing is between 650° C. and 800° C. when the flame is scanned along the internal surface of the preform toward an opening of the preform.