A memory cell array has a number of memory cells which are connected to word lines and bit lines and are arranged in a matrix form, each of the memory cells storing one of n levels (n is a natural number of 2 or more). A control circuit controls the potentials on the word lines and the bit lines in accordance with input data to write data to the memory cells. The control circuit is adapted to, at the write time, first apply a first potential to a well region or substrate in which the memory cells are formed, then set the well region or substrate to a second potential lower than the first potential, and next apply a predetermined voltage to the word lines to thereby perform a write operation.