Unsaturated poly (butylene adipate-co-butylene itaconate) (PBABI) copolyesters were synthesized through melt polymerization composed of 1,4-butanediol (BDO), adipic acid (AA), itaconic acid (IA) and 1,2,4,5-benzenetetracarboxylic acid (BTCA) as a cross-linking modifier. The melting point, crystallization and glass transition temperature of the PBABI copolyesters were detected around 29.8–49 °C, 7.2–29 °C and −51.1 and −58.1 °C, respectively. Young’s modulus can be modified via partial cross-linking by BTCA in the presence of IA, ranging between 32.19–168.45 MPa. Non-isothermal crystallization kinetics were carried out to explore the crystallization behavior, revealing the highest crystallization rate was placed in the BA/BI = 90/10 at a given molecular weight. Furthermore, the thermal, mechanical properties, and crystallization rate of PBABI copolyesters can be tuned through the adjustment of BTCA and IA concentrations.