According an embodiment, a semiconductor memory device includes a semiconductor memory chip to store plural pieces of data that are written and read in units of a page and are erased in units of a block including plural pages; a discarding unit to discard, after the data is written in the semiconductor memory chip with a logic address being designated, at least a portion of valid data among the plural pieces of data; a compaction unit to write the valid data excluding the discarded data in a second block among the valid data stored in a first block and erase the first block; and a controller to output, in response to a request for reading the discarded data, a response indicating that the data is unable to be read. When all the valid data included in a block are discarded, the discarding unit erases the block.