Poly(lactic acid) (PLA) is a biodegradable polymer with limited application because of its intrinsic brittleness, low toughness, and low elongation at break. Melt blends were prepared by mixing a natural rubber (NR, poly(1,4‐cis‐isoprene) in the form of liquid NR (LNR), liquid‐epoxidized NR (LENR), and polypropylene (PP) in the PLA matrix. Four blend systems were designed and prepared, i.e., PLA–PP, PLA–PP–LNR, and PLA–LNR or PLA–LENR. The composition of PP in the blend was fixed at 10 % PLAPP (90/10). Results showed that PLA–PP mixed with LNR improved impact and elongation at break. The binary blend of PLA–LNR (90/10) significantly enhanced impact strength and elongation at break properties. In contrast, the binary blends of PLA–LENR (90/10) showed a lower value of elongation at break (9.5 % vs. 37.3%) and impact strength (4.56 kJ m−2 vs. 6.44 kJ m−2). The melting temperature (Tm) and the glass transition temperature (Tg) were measured by differential scanning calorimetry, which recorded slight changes in the glass temperatures and melting temperatures. Scanning electron microscopy images of the tensile fracture of the PLA–LNR (90/10) blend showed the presence of large fibrils associated with the ductile failure related to neat PLA. Finally, the fracture toughness (KIC) of PLA–LNR (90/10) showed an increase of 39 % over neat PLA (2.94 MPa.m1/2 vs. 4.08 MPa.m1/2).