Springs store mechanical energy similar to batteries storing electrical energy. However, conventional springs are heavy and store limited amounts of mechanical energy relative to batteries, i.e they have low mass-energy-density. Next-generation 3D printing technology could potentially enable manufacturing low cost lightweight springs with high energy storage capacity. Here we present a novel design of a high-energy-density 3D printed torsional spiral spring using structural optimization. By optimizing the internal structure of the spring we obtained a 45% increase in the mass energy density, compared to a torsional spiral spring of uniform thickness. Our result suggests that optimally designed 3D printed springs could enable robots to recycle more mechanical energy per unit mass, potentially reducing the energy required to control robots.