A synapse memory system includes a plurality of synapse memory cells, a write portion, and read drivers. Each synapse memory cells is disposed at cross points of axon lines and dendrite lines and includes a plurality of analog memory devices and each synapse memory cell is configured to store a weight value according to an output level of a write signal. The plurality of analog memory devices is combined to constitute each synapse memory cell. The write portion is configured to write the weight value to each synapse memory cell and includes a write driver and an output controller. The write driver is configured to output the write signal to each synapse memory cell and the output controller is configured to control the output level of the write signal of the write driver. The read drivers are configured to read the weight value stored in the synapse memory cells.