1. A nonvolatile semiconductor memory device comprising: a memory cell array which includes a memory cell string including a plurality of memory cells each having a variable resistor element and a switching element having a current path with one end and the other end, between which the variable resistor element is connected, the plurality of memory cells having current paths thereof being connected in series, the memory cell array further including a first select element connected to one end of a current path of the memory cell, and a second select element connected to the other end of the current path of the memory cell; a bit line which is electrically connected to one end of a current path of the first select element; and a source line which is electrically connected to one end of a current path of the second select element.