Provided herein may be a controller and a data storage system having the controller. The controller may include a mapping time generator configured to generate a first mapping time at which a logical block address and a physical block address are mapped to each other, an internal memory configured to store first address mapping information including an address map, and the first mapping time, a host interface configured to transmit the first address mapping information to a host, and receive second address mapping information from the host, and a central processing unit configured to generate the address map, store the first address mapping information in the internal memory, compare a second mapping time included in the second address mapping information with the first mapping time, and select a read mode based on a result of the comparison.