A fiber modifier for improving thermo-bonding affinity of a composite fiber to a natural fiber includes a blend of maleic anhydride and a copolymer component selected from a copolymer of ethylene and acrylic acid, a copolymer of ethylene and methacrylic acid, and combinations thereof. A core and sheath composite fiber including a sheath component made from a fiber composition that contains the above fiber modifier is also disclosed.