An object is to provide a semiconductor memory device capable of shortening writing operation by concurrently determining potentials of memory cells on one word line. A plurality of transistors having switching characteristics are connected to one potential control circuit, whereby writing potentials are determined concurrently. A potential continues to be changed (raised or decreased) stepwise, a desired potential is determined while changing the potential, and whether data resulted from reading with respect to written data is correct or not is continuously checked, so that high-precision writing operation and high-precision reading operation can be achieved. In addition, favorable switching characteristics and holding characteristics of a transistor including an oxide semiconductor are utilized.