The present invention is related to a modified hydroxypolymer conjugates preferably a guanidine-dextran conjugate having a tumor cell killing activity. The modified hydroxypolymer conjugate is used as medicine, particularly for manufacturing a medicine or tumor killing composition for treating tumors. A method for producing said hydroxypolymer conjugate and a method for killing cancer cells and treating tumors is also disclosed. The invention is also related to a method for killing tumor cells and treating tumors by administering an effective amount of the modified hydroxypolymer conjugate.