Shape memory polymers are new model of intelligent polymers that can be able to recover their initial shape by external stimuli such PH,humidity,magnetic,heat,etc. SMPs must have two phases, one fixity phase and one recovery phase. Shape memory polymers could be formed and temporarily fixed in a second temporary shape. In the present work, the blend of SBS/LLDPE was used as the shape memory material. The diffrent amount of CNT were added to the blend and the blend were cured by DCP for improving the mechanical, thermal and SMP properties. Fixity and recovery of final samples were measured and improving of recovery were gained because of improvement of thermal conductivity of the blend caused by CNT. The mechanical properties, morphology and the rheological parameters of samples were obtained. The mechanical properties test were measured by tensile device at room temprature(23 C). The rheological properties measured by RMS device and the morphology of samples were obtained by SEM test.