Data from comprehensive thermomechanical tests of poly(L-lactide-co-epsilon-caprolactone) biodegradable shape memory polymer (SMP) reinforced with pristine and functionalized multiwalled carbon nanotubes (MWCNTs) are reported. The SMP specimens tested up to 500% strain and between 25 degrees C and 70 degrees C temperatures. The incorporation of functionalized MWCNTs leads to the best overall reinforcing effect in tensile modulus, yield stress, tensile strength and elongation at failure. Thermo mechanical experiments resulted that the functionalized MWCNTs increased the glass transition range of composites and changed the melting point of composites slightly. The crystallinity of composites was increased with increment of MWCNTs in composites. The shape fixity and shape recovery of composites increased slightly, while the recovery stress increased 46%. It is found that the functionalized MWCNTs prepare an effective physical cross linking and switching segments in polymer composites.