Poly (cyclohexanedimethanol cyclohexanedicarboxlic acid) (PCC), a fairly newly synthesized polyester, has been studied. Having a good experience of increasing both thermal stability and service temperature when applied to typical polymers, poly (tetramethylene glycol) (PTMG) was selected as a softening agent that was randomly copolymerized into the PCC chains. Another widely-used polyester, poly (ethylene terephthalate) (PET) was also produced in order to investigate the effect of PTMG, which was compared with the properties of the newly developed random PCC-PTMG copolymers (PCCP). In this study, the crystalline structures, the thermal and the mechanical properties of both PCC and PET containing different ratios of the random segment of PTMG were investigated by differential scanning calorimetery (DSC) and tensile tester. It was found that the crystallization rate of pure PCC was significantly slow, whereas for PCCP, PTMG effectively accelerated the crystallization rate with increasing PTMG, and the sample with 25 wt% of PTMG had the fastest crystallization rate in all PCCP samples. Here, the PTMG acted as an accelerator, simultaneously depressing the movement of PCC molecular chains. The elastic recovery test indicated that the ability of PTMG as a softening agent was highly demonstrated at 20 wt% of PTMG. The results of PCCP were compared with those of PET-PTMG copolymers (PETP) and it was found that there were optimum values of PTMG for the crystallization rate on both samples. Additionally, the results of the elastic recovery test indicated that the softening effects observed in PCCP were more pronounced than those observed in PETP.