Two-dimensional (2-D) hexagonal boron nitride (h-BN) has attracted considerable attention for deep ultraviolet optoelectronics and visible single photon sources, however, realization of an electrically-driven light emitter remains challenging due to its wide bandgap nature. Here, we report electrically-driven visible light emission with a red-shift under increasing electric field from a few layer h-BN by employing a five-period Al2O3/h-BN multiple heterostructure and a graphene top electrode. Investigation of electrical properties reveals that the Al2O3 layers act as potential barriers confining injected carriers within the h-BN wells, while suppressing the electrostatic breakdown by trap-assisted tunneling, to increase the probability of radiative recombination. The result highlights a promising potential of such multiple heterostructure as a practical and efficient platform for electrically-driven light emitters based on wide bandgap two-dimensional materials.