Disclosed is a cross-chain communication method. In this method, a first edge node of a first blockchain receives a first transaction request and validates the first transaction request; on condition that the first transaction request passes the validation, the first edge node will send the first transaction request to a notary node group; the notary node group determines at least one target notary node according to a preset criterion; the at least one target notary node validates the first edge node and a second edge node of a second blockchain corresponding to the first transaction request; and on condition that both the first edge node and the second edge node pass the validation, the first edge node will set up a cross-chain communication with the second edge node depending on the first transaction request to complete a cross-chain transaction. A cross-chain communication device and a storage medium are also disclosed.