Linear 1,10-decanediamine was chosen as a modified monomer to prepare modified poly(ethylene terephthalate) (PET) with a low content of amide bonds through two different synthetic methods. To evaluate the effect of amide bonds on the properties of poly(ester amide) analogs (PETAs), the performance of this new type of PET was compared with 1,10-decanediol-modified PET as a control group. The formation of hydrogen bonds in the PETAs was confirmed, and the stability of hydrogen-bonding interactions based on the low content of amide bonds at high temperature was discussed. Interestingly, physical cross-linking networks formed by hydrogen-bonding interactions improved the thermal stability, rheology, and mechanical properties of the PETAs. The crystallization properties were studied in depth by a series of tests, the results of which illustrated that the low content of amide bonds acted as a critical crystallization accelerator in the PETAs. A feasible strategy to prepare high-performance PET, which may be used as a packaging material, was introduced in this work.