A semiconductor memory device comprises a memory cell array including plural memory cells provided at the intersections of plural first lines and plural second lines; and a write circuit. The write circuit, on execution of a write operation, executes a first step of applying a voltage across the first and second lines connected to a data-write-targeted, selected memory cell, and a different voltage across the first and second lines connected to a data-write-untargeted, unselected memory cell of the plural memory cells and, after execution of the first step, executes a second step of applying a voltage, required for data write, across the first and second lines connected to the selected memory cell, and bringing at least one of the first and second lines connected to the unselected memory cell into the floating state.