According to one embodiment, a memory system writes data to a first block, and executes a garbage collection when the number of free blocks is not greater than a first threshold value. The memory system calculates a first number which is a ratio of the number of copy destination blocks needed for the garbage collection to the number of blocks to which data designated by a write command is written. The memory system determines whether the first number is greater than a second threshold value when a first command is received from the host, and performs fill-up processing for the first block when the first number is not greater than the second threshold value.