Poly($varepsilon$-caprolactone)-poly(ethylene glycol)-poly($varepsilon$-caprolactone) (PCL-PEG-PCL) multiblock copolymers at various hydrophobic-hydrophilic ratios were successfully synthesized by the chain extension of triblock copolymers through isocyanate (hexamethylene diisocyanate). Biodegradable films were prepared from the resulting multiblock copolymers using the casting method. The mechanical properties of the films were improved by chain extension of the triblock copolymers, whereas the films prepared by the triblock copolymers were weak and brittle. Atomic force microscopy (AFM) of the multiblock copolymer film showed that the hydrophilic PEG had segregated on the film surface. This is consistent with the observed contact angle of the films.