A synapse memory system includes: synapse memory cells provided at cross points of axon lines and dendrite lines, each synapse memory cell being associated with nonvolatile random-access memory (NVRAM), each synapse memory cell being configured to store a weight value according to an output level of a write signal; a write portion configured to write the weight value to each synapse memory cell, the write portion including a write driver and an output controller, the write driver being a digital driver configured to output the write signal to a subject synapse memory cell, the output controller being configured to control the output level of the write signal of the write driver; and read drivers configured to read the weight value stored in the synapse memory cells.