The present invention suggests a storage system capable of realizing highly reliable data back-up.The storage system includes: a first disk array apparatus for providing first volumes for storing data sent from a host system; a second disk array apparatus for providing second volumes for storing back-up data of the first volumes; and a console terminal for operating the first disk array apparatus. The console terminal is equipped with a setting unit for setting a priority for each first volume in accordance with an external command. The first disk array apparatus is equipped with: a storage unit for storing the priorities set by the priority setting unit; and a transfer unit for reading the priorities from the storage unit upon receiving the data and transferring the data stored in the first volumes to the second volumes of the second disk array apparatus in order of descending priority of the first volumes that store the data.