Fast, low-cost and efficient energy storage technologies are urgently needed to balance the intermittence of sustainable energy sources. High-power capacitors using organic polymers offer a green and scalable answer. They require dielectrics with high permittivity (εr) and breakdown strength (EB), which bio-based poly(hydroxy urethane)s (PHUs) can provide. PHUs combine high concentrations of hydroxyl and carbamate groups, thus enhancing their εr, and a highly tuneable glass transition (Tg), which dictates the regions of low dielectric losses. By reacting erythritol dicarbonate with bio-based diamines, fully bio-based PHUs were synthesised with Tg ~ 50 °C, εr > 8, EB > 400 MV·m-1 and low losses (tan δ < 0.03). This results in energy storage performance comparable with the flagship petrochemical materials (discharge energy density, Ue > 6 J·cm-3) combined with a remarkably high discharge efficiency (η = 85%). These bio-based PHUs thus represent a highly promising route to green and sustainable energy-storage.