A large payload bidirectional quantum secure direct communication (BQSDC) protocol without information leakage is proposed, which is based on entanglement swapping between any two Greenberger-Horne-Zeilinger (GHZ) states. Two remote authorized parties, Alice and Bob, can safely exchange their individual secret messages without worrying about the information leakage problem. Our protocol uses a shared secret GHZ state to overcome the information leakage problem. The shared secret GHZ state plays two roles in the bidirectional communication process: on one hand, it lets Bob know the prepared initial state; on the other hand, it is used for encoding Bob's secret messages. Moreover, our protocol can transmit six bits of secret messages per round communication. Compared with those previous BQSDC protocols, the advantage of our protocol lies in having the following two characters simultaneously: on one hand, it overcomes the information leakage problem; one the other hand, its capacity is as high as six bits per round communication.