This work reports the reversible shape memory polymer (RSMP) by semicrystalline poly(ethylene-co-vinyl acetate) (PEVA) with dynamic covalent polymer networks. The ester linkages in the cross-linked PEVA acted as dynamic covalent bonds in the presence of a transesterification catalyst. This dynamic covalent network imparted the material with good thermal plasticity in a non-flow state at high temperature. The resulting PEVA possessed both the reversible shape memory effect (RSME) and thermadapt property. The thermadapt performance gave little adverse effect on the RSME. This work provides an approach to improve the reprocessability/recyclability of thermoset RSMPs through simple modification of commercially available polymers.