The recent rapid development of soft electronics and wearable technology has demanded materials with the function of combining mechanical deformation and electronics. Particularly, materials simultaneously having memory shape characteristics in which mechanical deformation repeatedly occurs in response to stimulus, high stretchability and excellent electric/heat transfer characteristics are interesting actuator materials in future applications. As a stretchable and conductive platform, we fabricated a reentrant micro-honeycomb structure from graphene-CNT, which had structural stretchability due to the accordion-like reentrant structure and continuous conductive paths in the vertical and horizontal directions. To impart shape memory properties, we fabricated composites by simply infiltrating shape memory polyurethane (SMPU) into a stable graphene/CNT framework. Our resulting reentrant micro-honeycomb graphene-CNT/SMPU composites simultaneously exhibited a relatively low resistivity of 5 Ω cm, a change in resistance of less than 10% in the 50% stretching/releasing states, long term stability, and superior tensile shape memory properties, including 95.6% shape fixity and a 90.6% recovery ratio. Regularly distributed graphene-CNT structures offer heterogeneous nucleation sites and undisturbed crystal growth in neat SMPU pillars, resulting in superior shape memory properties. We also constructed a circuit with portable batteries to demonstrate that our reentrant graphene-CNT/SMPU composite offers potential applications as an emergency circuit breaker.