Thermal diodes(1,2)-devices that allow heat to flow preferentially in one direction-are one of the key tools for the implementation of solid-state thermal circuits. These would find application in many fields of nanoscience, including cooling, energy harvesting, thermal isolation, radiation detections and quantum information(4), or in emerging fields such as phononics(5-7) and coherent caloritronics(8-10). However, both in terms of phononic(11-13) and electronic heat conduction(14) (the latter being the focus of this work), their experimental realization remains very challenging(15). A highly efficient thermal diode should provide a difference of at least one order of magnitude between the heat current transmitted in the forward temperature (T) bias configuration (J(fw)) and that generated with T-bias reversal (J(rev)), leading to R = J(fw)/J(rev) >> 1 or << 1. So far, R approximate to 1.07-1.4 has been reported in phononic devices(16-18), and R approximate to 1.1 has been obtained with a quantum-dot electronic thermal rectifier at cryogenic temperatures19. Here, we show that unprecedentedly high ratios of R approximate to 140 can be achieved in a hybrid device combining normal metals tunnel-coupled to superconductors(20-22). Our approach provides a high-performance realization of a thermal diode for electronic heat current that could be successfully implemented in true low-temperature solid-state thermal circuits.