Linear and star-shaped, poly(lactic acid) (PLA) stereo-block copolymers were synthesized by sequential polymerization of DL-lactic acid and L-lactide in the presence of diol or polyol compounds. The molecular weight of block copolymers could be controlled to some extent by the variation of alcohol content. These block copolymers had relatively narrow molecular weight distributions. The glass transition temperature and melting temperature of block copolymers appeared at around 5$0^{circ}C$ and 100~14$0^{circ}C$, respectively. The block copolymers were found to crystallize even at the high D-stereoisomer concentration of 35 mol%, in contrast to the amorphous nature of the random copolymer with similar composition. Also we could observe the crystallinity of PLA stereo-block copolymers varying with annealing temperature and time.