A semiconductor memory includes a semiconductor substrate, a buried insulating film formed on a part of an upper surface of the semiconductor substrate, and a semiconductor layer formed on another part of the upper surface of the semiconductor substrate. Each of the memory cell transistors comprises a first-conductivity-type source region, a first-conductivity-type drain region, and a first-conductivity-type channel region arranged in the semiconductor layer in the column direction, and a gate portion formed on a side surface of the channel region in the row direction.