1. A semiconductor memory device, comprising: a memory cell array including a memory cell layer, said memory cell layer containing plural first lines, plural second lines intersecting said first lines, and plural memory cells provided at the intersections of said plural first lines and second lines and operative to store data in accordance with different resistance states; and an access circuit operative to make access to said memory cells via said first lines and second lines, said memory cell changing said resistance state from a first resistance state to a second resistance state on application of a certain voltage of a first polarity, and changing said resistance state from a second resistance state to said first resistance state on application of a certain voltage of a second polarity opposite in polarity to said first polarity, and said access circuit applying voltages, required for access to said memory cell, to said first line and said second line connected to a selected memory cell, and bringing at least one of said first lines and said second lines connected to non-selected memory cells into a state in which a certain potential is not supplied/applied from external to make access to said selected memory cell, wherein said access circuit, on a first access operation for making access to said selected memory cell, sets said plural first lines and said plural second lines to a first voltage, then sets said plural first lines or said plural second lines to a second voltage higher than said first voltage, then sets said first line connected to said selected memory cell to a third voltage equal to or higher than said second voltage, sets said second line connected to said selected memory cell to said first voltage, and brings at least one of said first lines and said second lines connected to said non-selected memory cells into the floating state.