We demonstrate that two-dimensional (2D) arrays of coupled quantum dots (QDs) with six-fold degenerate p orbitals (including spin degeneracy) can display bistable states, suitable for application in high-density memory device with low power consumption. Due to the inter-dot overlap of px,y orbitals in these QD arrays, two dimensional conduction bands can be formed in the x–y plane, while the pz orbitals remain localized in the x–y plane such that the coupling between pz orbitals located at different dots can be neglected. We model such systems by taking into account the on-site repulsive Coulomb interactions (U) between electrons in any of the three p orbitals, which also lead to a coupling between the localized pz orbitals with the 2D conduction bands formed by px/py orbitals. The Green's function method within an extended Anderson model is used to calculate the tunneling current through the QDs. We find that bistable tunneling current can exist for such systems due to the interplay of the on-site Coulomb interactions between the pz orbitals and the delocalized nature of conduction band states derived from the hybridization of px/py orbitals. This bistable current depends critically on the strength of U, the band width, and the ratio of the left and right tunneling rates. The behavior of the electrical bistability can be sustained when the 2D QD array reduces to a one-dimensional (1D) QD array, indicating the feasibility for high-density packing of these bistable nanoscale structures.