Cryptography is the science of using mathematics to encrypt and decrypt the data for secure communication. It enables the user to transmit the data in insecure network so that it cannot be read by anyone except the intended recipient. RSA and Elliptic Curve Cryptography are the existing public key cryptography technique which is used to provide secure data transmission. Existing DNA based cryptography technique need more computational power and more processing time with larger key sizes to provide higher level of security. This imposes a limitation on public key cryptography scheme. In order to overcome this limitation, a new cryptographic scheme is proposed which provides first level of security with smaller key size and less computation overhead using DNA Computing technique. The second level of security is provided by using low computation ECC encryption and decryption algorithm. The novelty of this proposed scheme is advantages of both ECC and DNA computation is exploited in providing a high level of data security. Finally, the performance of cryptography scheme is compared with the existing cryptographic schemes.