The use of bio-based polymers in place of conventional polymers gives positives effects in the sense of reduction of environmental impacts and the offsetting of petroleum consumption. As such, in this study, jatropha oil was used to prepare epoxidized jatropha oil (EJO) by the epoxidation method. The EJO was used to prepare a shape memory polymer (SMP) by mixing it with the curing agent 4-methylhexahydrophthalic anhydride (MHPA) and a tetraethylammonium bromide (TEAB) catalyst. The resulting bio-based polymer is slightly transparent and brown in color. It has soft and flexible properties resulting from the aliphatic chain in jatropha oil. The functionality of SMP was analyzed by Fourier transform infrared (FTIR) spectroscopy analysis. The thermal behavior of the SMP was measured by thermogravimetric analysis (TGA), and it showed that the samples were thermally stable up to 150 °C. Moreover, the glass transition temperature characteristic was obtained using differential scanning calorimetry (DSC) analysis. The shape memory recovery behavior was investigated. Overall, EJO/MHPA was prepared by a relatively simple method and showed good shape recovery properties.