Poly(l‐lactic acid) (PLLA) was blended with a series of four‐armed poly(ϵ‐caprolactone)‐block‐poly(d‐lactic acid) (4a‐PCL‐b‐PDLA) copolymers in order to improve its crystallization rate and mechanical properties. It is found that a higher content of 4a‐PCL‐b‐PDLA copolymer or longer PDLA block in the copolymer lead to faster crystallization of the blend, which is attributed to the formation of stereocomplex crystallites between PLLA matrix and PDLA blocks of the 4a‐PCL‐b‐PDLA copolymers. Meanwhile, the PDLA block can improve the miscibility between flexible PCL phase and PLLA phase, which is beneficial for improving mechanical properties. The tensile results indicate that the 10% 4a‐PCL5k‐b‐PDLA5k/PLLA blend has the largest elongation at break of about 72% because of the synergistic effects of stereocomplexation between enantiomeric PLAs, multi‐arm structure and plasticization of PCL blocks. It is concluded that well‐controlled composition and content of 4a‐PCL‐b‐PDLA copolymer in PLLA blends can significantly improve the crystallization rate and mechanical properties of the PLLA matrix. © 2017 Society of Chemical Industry