Biodegradable four-arm star-shaped poly(lactic acid) (4sPLA) was synthesized from L-Lactic acid ( L-LA) and pentaerythritol (PENTA), and the polymerization kinetics was studied. The effects of reaction time, reaction temperature and molar ratio on the polymerization of 4sPLA were discussed. The molecular structure of 4sPLA was characterized by Fourier transform infrared spectroscopy (FTIR) and 1H nuclear magnetic resonance spectra ( 1 H-NMR). The results showed that the optimum reaction conditions were as follows: the molar ratio of L-LA to PENTA was 12:1, and the polymerization reaction occurred at 160 ℃ for 5 h. Gel permeation chromatography (GPC) method was used to determine the polymerization kinetics of 4sPLA consistent with the first-order reaction kinetics.