Branched poly(butylene succinate) (PBS) copolymers were synthesized, from succinic acid (SA), 1,4-butanediol (1,4-BD), and 1,2-octanediol (1,2-OD) through a two-step process containing esterification and polycondensation, with different mole fractions of 1,2-OD segments. The branched PBS copolymers were characterized with 1 H-NMR, differential scanning calorimetry (DSC), wide angle X-ray diffraction (WAXD), thermogravimetric analysis (TGA), dynamic rheological testing, and tensile properties analysis. The results of DSC and WAXD show that, with the increasing of the 1,2-OD segments content, the glass transition temperature (T g ), melting temperature (T m ), crystallization temperature (T c ), and the degree of crystallinity (X c ) decrease. While the crystal structure of PBS does not change by introducing 1,2-OD segments. The results of TGA and dynamic rheological testing indicate that the thermal stability of neat PBS is improved with the addition of 1,2-OD segments. The incorporation of 1,2-OD segments has some effects on the rheological properties of PBS, such as complex viscosities (|g*|), storage modulus (G 0 ), and loss modulus (G 00 ). Tensile testing demonstrates that the elongation at break is improved significantly with increasing 1,2-OD segments content, but without a notable decrease of tensile strength.