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Recent breakthroughs in Josephson diodes dangle the possibility of extending conventional non-reciprocal electronics into the realm of superconductivity. While a strong magnetic field is recognized for enhancing diode efficiency, it concurrently poses a risk of undermining the essential superconductivity required for non-dissipative devices. To circumvent the need for magnetic-based tuning, we propose a field-effect Josephson diode based on the electrostatic gate control of finite momentum Cooper pairs in asymmetric spin-momentum-locking states. We propose two possible implementations of our gate-controlled mechanism: (i) a topological field-effect Josephson diode in time-reversal-broken quantum spin Hall insulators; and (ii) semiconductor-based field-effect Josephson diodes attainable in current experimental setups involving a Zeeman field and spin-orbit coupling. Notably, the diode efficiency is highly enhanced in the topological field-effect Josephson diode because the current carried by the asymmetric helical edge states is topologically protected and can be tuned by local gates. In the proposed Josephson diode, the combination of gates and asymmetric spin-momentum-locking nature is equivalent to that of a magnetic field, thus providing an alternative electrical operation in designing nonreciprocal superconducting devices.