As an active heat transfer enhancement technique, electrohydrodynamic has excellent potential to enhance the melting rate during solid–liquid phase change. In this work, the lattice Boltzmann method is adopted to investigate the electrohydrodynamic enhancement of solid–liquid phase change in three-dimensional cavities. The numerical method is firstly validated by several carefully chosen test cases, and then we conducted simulations under different governing parameters and aspect ratios. Results show that the interface morphologies obtained from pure electro-convection and pure thermo-convection are significantly different due to the different directions of the buoyancy and Coulomb forces. Besides, the augmentation of melting due to the electric effect becomes significant when the electric driving parameter T increases. For sufficiently high values of T, the melting performance is mainly dominated by the Coulomb force, and the influence of the thermal Rayleigh number in such a case is insignificant. Further, we note that the melting performance in the enclosure depends on the aspect ratio, and the lateral wall in a three-dimensional cavity with a relatively smaller aspect ratio usually inhibits the electro-convection. Finally, a comparison between the two-dimensional and three-dimensional simulations shows that the added dimension significantly affects the flow dynamics and the interface shape, which cannot be ignored for similar problems.