The invention belongs to the technical field of polyester preparation, and discloses a modified PET copolyester with high viscosity and a low terminal carboxyl group and a preparation method and application thereof. The copolyester contains the following ingredients in parts by weight: 100 parts of low-viscosity PET copolyester, 0.8-2.0 parts of oxazoline compound and 0.6-2.0 parts of a hydroxyl chain extender. The method prepares the high-viscosity modified PET copolyester by adding the oxazoline compound and the hydroxyl chain extender. The oxazoline compound is added to react with the terminal carboxyl group in resin, the terminal carboxyl group content of resin is reduced, therefore, the hot water resisting performance of resin is increased. The hydroxyl chain extender is added, the molecular weight of resin is increased, and the balance between a physical performance and a processing performance is achieved. The viscosity and the melt strength of the modified PET copolyester are increased, the content of terminal carboxyl group is reduced, and the hot water resisting performance is greatly increased. Moreover, the production method shortens the polycondensation time and the production cycle, effectively reduces the thermal degradation reaction, and also increases the output of equipment.