The paper presents a hybrid cryptographic method combining machine learning through modified Hebbian neural networks (MHNN) and DNA computing to secure data transmission over open networks. It introduces a two-phase process involving a sender and receiver: the sender encrypts the plaintext using an MHNN and compresses it with DNA coding, while the receiver decrypts the message with a reverse operation. The proposed system aims to enhance data security against unauthorized access and eavesdropping, demonstrating effectiveness and efficiency in protecting transferred data.