With the growing importance of transmitting data over the network, data encryption is becoming critical. Encryption helps safeguarding the data transmitted over the network from an unwanted entity. The two methods to encrypt data are-Substitution and Transposition. Transposition refers to changing the position of characters in a given text. On the other hand, substitution is the process of replacing each character of the plaintext with some other character. Playfair cipher is an illustration of substitution cipher. The classical playfair cipher has a 5x5 matrix. To increase the resistance of playfair cipher, this paper proposes to introduce double Myszkowski transposition on a modified 6x6 playfair matrix. The 6x6 matrix includes the all the alphabets along with the single digit numbers. A comparison with the classical 5x5 playfair cipher proves the enhanced security of the proposed algorithm.