1. A nonvolatile semiconductor memory device, comprising: a memory cell array including a plurality of first lines, a plurality of second lines intersecting the plurality of first lines, and a plurality of memory cells provided one at each of intersections of the plurality of first lines and the plurality of second lines and each storing data by a data storing state of a filament; and a control circuit configured to execute a write sequence that writes data to the memory cell, the write sequence including: a setting operation that applies a setting pulse having a first polarity to the memory cell; and a removing operation that applies a removing pulse having a second polarity opposite to the first polarity to the memory cell; and the control circuit, during execution of the write sequence, is configured to repeatedly execute the setting operation until the memory cell attains a desired data storing state, and then to execute the removing operation.