Cryptography can be considered one of the most important aspects of communication security with existence of many threats and attacks to the systems. Unbreakableness is the main feature of a cryptographic cipher. In this thesis, feasibility of using neural networks, due to their computational capabilities is investigated for designing new cryptography methods. A newly proposed block cipher based on recurrent neural networks has also been analysed It is shown that: the new scheme is not a block cipher, and it should be referred to as a symmetric cipher; the simple architecture of the network is compatible with the requirement for confusion, and diffusion properties of a cryptosystem; the back propagation with variable step size without momentum, has the best result among other back propagation algorithms; the output of the network, the ciphertext, is not random, proved by using three statistical tests; the cipher is resistant to some fundamental cryptanalysis attacks, and finally a possible chosen-plaintext attack is presented.