A series of biodegradable SMP networks with various PCL arm lengths and well-defined star-branched molecular structures were fabricated using polyhedral oligomeric silsesquioxane (POSS) as the core reacting with different molecular weight PCL. Fourier transform infrared spectroscopy (FTIR) was used to follow the reaction, and the cross-link density of the samples was evaluated by the gel content. Differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) results showed a similar trend: transition temperature can be tailored by varying the PCL molecular weight; melting temperature of the networks gradually increased with increasing of the PCL molecular weight. The crystallization behavior was studied by DSC and the crystallization temperatures of these networks were influenced by PCL arm lengths. Mechanical properties of the POSS–PCL networks at two different temperatures were compared: tensile strength reaching 12 MPa at room temperature while this figure reduced to around 0.1 MPa above its transition temperature. Outstanding shape memory behaviors of the samples were observed in the strain-controlled cyclic thermomechanical tensile test. The results revealed that sample POSS-N2000 (higher POSS moiety) displayed the most remarkable shape fixity (97%) and recovery ratio (99%), which was induced by lowering the cross-linking density and increasing chain mobility. Finally, the possible molecular mechanism of shape memory was illustrated schematically.