A semiconductor memory device includes a first memory cell for storing data using at least three levels of threshold voltages, including a first level, a second level higher than the first level and a third level higher than the second level. A first word line is connected to the first memory cell. In writing of data to the first memory cell from a state where a threshold voltage of the first memory cell is the first level, a plurality of program operations and verify operations are performed, each program operation including applying a program voltage to the first word line, each verify operation including applying a read voltage lower than the program voltage. The program operations include a program operation for the second level and a program operation for the third level, and the verify operations include a verify operation for the second level, and do not include a verify operation for the third level.