AbstractPoly(3‐hydroxybutyrate‐4‐hydroxybutyrate) (P34HB) copolyester is a new type of biodegradable polymer material, but it cannot meet the market requirements because of its poor thermal stability. In this work, P34HB with a low degree of cross‐linking was successfully prepared by incorporating a small amount of a multiple epoxy chain extender, known as Joncryl ADR‐4380 (styrene‐methacrylic acid glycidyl ester copolymer), through reactive extrusion. The rheological properties, thermal stability, thermal behavior, and mechanical properties of the materials were investigated. Fourier transform infrared spectroscopy and gel content test showed that there was a significant chemical interaction between P34HB and ADR4380, and a cross‐linked structure was produced. Compared with pure P34HB, the samples after chain extension showed improved rheological properties, with increased viscosity and melt elasticity due to the formation of a gel network. Thermogravimetric analysis, dynamic time scanning experiment, and melt flow index (MFI) provided strong evidence for the enhanced of thermal stability of P34HB. The onset decomposition temperature of P34HB increased by 13.5°C, and its MFI decreased from 23.30 to around 5 at 170°C, and the complex viscosity remained relatively stable with time after modification. In terms of mechanical properties, the maximum elongation at break increased by 88.08% due to the improvement of toughness.