A novel thermosensitive block copolymer composed of poly(ethylene glycol) (PEG) and poly($N$-($N$-Boc- ethylenediamine)methacryloylglycylglycylamide) (PBEMAGG) with pendant amino groups was synthesized via reversible addition-fragmentation chain transfer (RAFT) polymerization. The thermosensitivity of these copolymers was studied with varying temperatures and block lengths of copolymers. The results indicated that the lowest critical solution temperatures (LCST) of this thermosensitive copolymer cover the range from $20^{circ}C$ up to near $45^{circ}C$, and can be easily and precisely regulated by changing the block length or the amount of pendant amino groups. This copolymer with well-controlled LCST and pendant functional groups shows great potential for use as a smart drug-delivery system.