Extrusion of Poly(lactic acid) (PLA) is difficult to carry out due to the brittleness and low melt strength of PLA. In this investigation, linear Poly(lactic acid) (L-PLA) and branched (B-PLA) were plasticized with poly(ethylene glycol) (PEG) having $M_w$ of 1,000 g/mol in various PEG concentrations (0, 5, 10, 15 and 20 wt%). In addition rheological, thermal and mechanical properties were also investigated in this study. In relation to the plasticizer content, dynamic rheological studies showed that the plasticized linear and branched PLA with higher PEG loading have lower viscosity and elastic properties than that of pure PLA. Storage modulus decreased with PEG loading at all frequencies and exhibited weak frequency dependence with increasing PEG content. As expected, plasticizing both linear and branched PLA lowered the glass transition temperature and modified the crystallization characteristics. Moreover, the toughness was increased by plasticizing up to 15 wt% of B-PLA and up to 10 wt% of L-PLA. However, there was decreasing in toughness due to phase separation of PEG phase in the PLA matrix at 20 wt% and 15~20 wt% of B-PLA and L-PLA, respectively. Therefore, the combination usage of branching and plasticizing showed the better properties both the melt stability and the ability to plastic deformation of PLA to meet the requirements for further.