Compared with their three-dimensional counterparts, low-dimensional metal halide perovskites with periodic inorganic/organic structures have shown promising stability and hysteresis-free electrical performance, which paves the way for next-generation optoelectronic devices. However, when integrated in devices, they have relatively limited efficiencies because devices usually require carrier transport through the film thickness direction. In conventionally grown single crystals, the carrier transport in the thickness direction is hindered by the insulating organic spacers. In addition, the strong quantum confinement from the organic spacers limits the generation and transport of free carriers. The carrier dynamics is further compromised by the presence of grain boundaries in polycrystals. Here, we report a low-dimensional metal halide perovskite superlattice with efficient carrier transport in three dimensions by epitaxial growth. Epitaxy on a slightly lattice-mismatched substrate compresses the organic spacers in the superlattice, which weakens the quantum confinement and further improves carrier dynamics. The performance of a low-dimensional perovskite superlattice solar cell has been certified under the quasi-steady state for the first time. Moreover, the device shows an unusually high open-circuit voltage, due to a unique intra-band exciton relaxation mechanism.