As a possible biocompatible and biodegrable polymer skeleton for drug delivery system, block copolymers of L-lactic acid and L-glutamic acid with different composition were synthesized and characterized. Poly (L-lactide) was prepared by polymerization of L-lactide with zine oxide at $130^{circ}C$ for 72 hrs. 3-Amino-l-propanol was introduced to poly (L-lactide) by an ester linkage in order to initiate polymerization. Polymerization of $gamma-benzyl-L-glutamate-N-carboxyanhydride(gamma-BLG-NCA)$ utiliizing the amino group of modified poly (L-lactide) as an initiator gave rise to the block copoly $(L-lactide-gamma-benzyl-L-glutamate).$ The NMR study of resulting block copolymers showed that the composition of L-lactic acid and $gamma-benzyl-L-glutamate$ in block copolymers was depended on the weight ratio of poly (L-lactide) and $gamma-BLG-NCA.$ The thermal properties of the resulting block copolymers were determined by the differential scanning calorimetry and by the thermogravimetry.