Through a two-step melt polycondensation method, three poly(ethylene succinate-co-ethylene suberate) (PESSub) copolymers containing different contents of ethylene suberate (ESub) from 4.8 to 15.3 mol % and with similar molecular weights were successfully synthesized in this research. To demonstrate the effect of the ESub composition, the crystallization kinetics, morphology, and mechanical properties of PESSub were systematically studied. The crystal structure of PESSub was the same as that of PES; however, with increasing ESub composition, the degree of crystallinity values slightly decreased. The increase of the ESub content led to a depression in the glass transition temperature, cold crystallization temperature, cold crystallization enthalpy, melting point, heat of fusion, and equilibrium melting point of PESSub. Increasing the ESub composition retained the crystallization mechanism but decreased the crystallization rates and spherulitic growth rates. The copolymers with higher ESub component showed greater elongation at break but smaller tensile strength and Young's modulus. The crystallization behavior and mechanical properties of the synthesized novel copolyesters were well-regulated by adjusting the content of the ESub units.