Polycaprolactone-polylactide block copolymers (PCL-block-PLA) were grafted onto filled multi-wall carbon nanotubes (MWCNT) successfully. In this synthesis, MWCNTs were opened and functionalized, and then they were filled by silver nanoparticles. The filled MWCNT were used as macroinitiator for ring opening polymerization of ε-caprolactone and L-lactide. Then the end hydroxyl functional groups of MWCNT-graft-PCL or MWCNT-graft-PLA were used as initiator for ring opening polymerization of lactide and ε-caprolactone and MWCNT-graft-PCL-block-PLA or MWCNT-graft-PLA-block-PCL were obtained, respectively. Length of grafted copolymer chains onto the MWCNT was controlled using CNT/monomer ratio. Nanocomposites' properties depend on the length of polymer blocks strongly. Structure of nanocomposites was evaluated by TEM and spectroscopy methods.