The present invention relates to the technical field of memories, and in particular to a highly-consistent resistive memory and method of fabricating the same. The resistive memory comprises: a lower electrode which is formed in a first dielectric layer by patterning; a second dielectric layer formed on the lower electrode and the first dielectric layer and provided with an opening for exposing the lower electrode to perform patterning; an edge wall formed in the opening of the second dielectric layer for covering a border area of the lower electrode and the first dielectric layer so that only the middle area of the lower electrode is partially or totally exposed; a storage medium layer formed by performing oxidization with the second dielectric layer and the edge wall as mask; and an upper electrode. The resistive memory exhibits good consistency and high reliability; moreover, unit size is mall, which is advantageous for improving storage characteristic. When an array of memories is formed by the resistive memories, a good consistency is obtained among multiple resistive memories.