A series of shape memory blends of natural Eucommia ulmoides gum (EUG) and low-density polyethylene (LDPE) with a bicontinuous cross-linked structure were prepared by a physical blending method, which could be used in the field of thermal response with two different temperatures. We report the shape memory properties of these blended materials with two response temperatures for the first time. The mechanical, curing, thermal and shape memory properties of the blends were studied in this manuscript. Schematic diagrams are proposed to illustrate the dual shape memory behaviors of the EUG/LDPE blends. Our study focused on observing the relationship between the shape memory behavior and the microscopic crystalline phase states in the blends. In the blends, both the cross-linked network and the LDPE crystalline regions could act as fixed domains, while the crystalline regions of LDPE or EUG could act as the reversible domain. The shape memory properties were mainly determined by the components of the fixed and reversible domains. We focused on the shape memory behavior of blends at 60 °C and 130 °C in this manuscript. The results showed that when the peroxide dicumyl peroxide (DCP) dosage was 1.0 phr, the blends exhibited acceptable shape behavior at 60 °C (R1f = 74.8%, R1r = 63.3%). At the same time, when DCP dosage was 0.4 phr, the shape memory behavior of the blends at 130 °C was good and much better than that at 60 °C (R2f = 91.1%, R2r = 89.4%).