Cryptography was used since ancient days where plain text or confidential message was converted to a message which is in unreadable format or cipher text using secret key and an encryption algorithm and cipher text is converted to plaintext using decryption algorithm and a secret key. Cryptography ensured secured communication of messages and also provided integrity, confidentiality and availability of the information RSA is an asymmetric algorithm most widely used since 1977. Researchers and cryptanalysis have looked for ways to attack RSA. Some common attacks on RSA are discussed in this research work. Objective – The Main objective of this research was to study RSA algorithm, its weakness and attacks on RSA and to work on to make existing RSA algorithm stronger. Attack like the chosen cipher text attack, partial key exposure attack, common modulus attack and low decryption exposure attack are frequently targeted attacks for RSA algorithm. Findings – RSA algorithm can be partially or fully cracked if not implemented correctly. Proposed Work – In this research a new algorithm has been proposed using two layer DNA cryptography [1] and proposed algorithm is added on the top of RSA algorithm to make the RSA algorithm stronger. Message is first encrypted with proposed two-layer DNA algorithm and output of this is input to RSA algorithm. Implications – Algorithm can be applied to encrypt small ATM pin, small secret messages etc. Result, Outcome and Originality - Security analysis of proposed system has proven good. Algorithm uses two-layer DNA cryptography with different function and encoding tables. Indian copyright is granted for the algorithm under the registration number L-120035/2022