PURPOSE: A prepolymer obtained by the melt polymerization of the reaction mixture containing a specific amount of a polyfunction compound is subjected to solid phase polycondensation reaction, the producing said polyester that can suitably used in direct blow molding because of its high melt viscosity with industrial advantage.

CONSTITUTION: In the production of a branched polyester mainly containing ethylene terephthalate units, a polyfunctional compound as trimelltic acid or pentaerythritol is added so that the amount satisfies equations I and II [b is the proportion of the polyfunctional compound in the copolymer (mol%); f is the number of functions of the polyfunctional compound, 3 or 4; V is the target intrinsic viscosity of the polyester] to produce a prepolymer of 0.4W0.8 intrinsic viscosity and the resulting prepolymer is subjected to solid phase polycondensation reaction to give said polymer with the target intrinsic viscosity. When needed, less than 10mol% of a difunctional compound as isophthalic acid, neopentyl glycol may be added as a copolymer component.