This paper proposes a new technique to encrypt data using DNA sequence. DNA Cryptography is a technique which is emerging almost every field of network security. The method proposed in this paper is an alternative approach of encryption using DNA sequence which is quite efficient in terms of both computational speed and security. Here along with the DNA encryption, RSA key exchange algorithm has been applied in order to exchange the keys between two dedicated parties to encrypt and decrypt the message. Here in the method, the original message is first converted to ASCII equivalent and then it is converted to DNA sequence using the table which represents a unique character for each binary combination. After that, a subsequence of the DNA sequence is selected using the key (contains interval to select the subsequence) and converts to its equivalent mRNA and then to tRNA. The remaining elements at the left and the right of the subsequence are swapped, and a new encrypted cipher is obtained which is transmitted over the network and then decrypted in the same way at the receiver’s end, and finally, the original text is again generated. This is an efficient way to encrypt the data as only a single key pair is exchanged to perform the encryption and decryption and no any highly computational operations are performed to maintain a good level of secrecy. Finally, the security analysis is performed which includes frequency analysis, Friedman randomness test, and RSA security analysis to present the security level of proposed method.