Chaotic systems are sensitive to initial conditions, system parameters and topological transitivity and these properties are also remarkable for cryptanalysts. Noise like behavior of chaotic systems is the main reason of using these systems in cryptology. However some properties of chaotic systems such as synchronization, fewness of parameters etc. cause serious problems for cryptology. In this paper, to overcome disadvantages of chaotic systems, the dynamics of Chua’s circuit namely x, y and z were modeled using Artificial Neural Network (ANN). ANNs have some distinctive capabilities like learning from experiences, generalizing from a few data and nonlinear relationship between inputs and outputs. The proposed ANN was trained in different structures using different learning algorithms. To train the ANN, 24 different sets including the initial conditions of Chua’s circuit were used and each set consisted of about 1800 input-output data. The experimental results showed that a feed-forward Multi Layer Perceptron (MLP), trained with Bayesian Regulation backpropagation algorithm, was found as the suitable network structure. As a case study, a message was first encrypted and then decrypted by the chaotic dynamics obtained from the proposed ANN and a comparison was made between the proposed ANN and the numerical solution of Chua’s circuit about encrypted and decrypted messages.