Resonant tunnelling is a quantum mechanical process that has long been attracting both scientific and technological attention owing to its intriguing underlying physics and unique applications for high-speed electronics. The materials system exhibiting resonant tunnelling, however, has been largely limited to the conventional semiconductors, partially due to their excellent crystalline quality. Here we show that a deliberately designed transition metal oxide superlattice exhibits a resonant tunnelling behaviour with a clear negative differential resistance. The tunnelling occurred through an atomically thin, lanthanum {delta}-doped SrTiO3 layer, and the negative differential resistance was realized on top of the bipolar resistance switching typically observed for perovskite oxide junctions. This combined process resulted in an extremely large resistance ratio (~10^5) between the high and low-resistance states. The unprecedentedly large control found in atomically thin {delta}-doped oxide superlattices can open a door to novel oxide-based high-frequency logic devices.