A semiconductor memory device is disclosed. The semiconductor memory device converts a sequentially-changing step voltage into a current so as to provide a write current, and minimizes the influence of a threshold voltage variation caused by fabrication deviation, such that it can be stably operated. The semiconductor memory device includes a current driver. The current driver includes a step voltage provider configured to provide a step control voltage sequentially changing in response to a pulse control signal, a control current provider configured to provide a control current in response to the step control voltage, and a write driver configured to provide a write current capable of writing data in a memory cell in response to the control current.