The majority of 3D-printed biodegradable biomaterials are brittle, limiting their potential application to compliant tissues. Poly (glycerol sebacate) acrylate (PGSA) is a synthetic biodegradable and biocompatible elastomer, compatible with light-based 3D printing. In this work we employed digital-light-processing (DLP)-based 3D printing to create a complex PGSA network structure. Nature-inspired double network (DN) structures with two geometrically interconnected segments with different mechanical properties were printed from the same material in a single shot. Such capability has not been demonstrated by any other fabrication technique. The biocompatibility of PGSA after 3D printing was confirmed via cell-viability analysis. We used a finite element analysis (FEA) model to predict the failure of the DN structure under uniaxial tension. FEA confirmed the soft segments act as sacrificial elements while the hard segments retain structural integrity. The simulation demonstrated that the DN design absorbs 100% more energy before rupture than the network structure made by single exposure condition (SN), doubling the toughness of the overall structure. Using the FEA-informed design, a new DN structure was printed and the FEA predicted tensile test results agreed with tensile testing of the printed structure. This work demonstrated how geometrically-optimized material design can be easily and rapidly achieved by using DLP-based 3D printing, where well-defined patterns of different stiffnesses can be simultaneously formed using the same elastic biomaterial, and overall mechanical properties can be specifically optimized for different biomedical applications.