An apparatus and a method are provided for transmitting a Hybrid Automatic Repeat reQuest ACKnowledgement (HARQ-ACK) in a Time Division Duplexing (TDD) Carrier Aggregation (CA) system, wherein the duplex direction of a sub frame may change flexibly. According to the method, a UE receives configuration information from a base station for each cell working under a CA mode; determines a distribution of fixed sub frames and flexible sub frames in each cell; determines timing of a HARQ-ACK for downlink transmission in each cell; and transmits the HARQ-ACK, based on the determined timing of the HARQ-ACK for each cell.