Encoding and Decoding of a transmitted data through the communication system is considered as an important subject that meets great efforts. It is well known that there are many types of the error control coding system; one of the most important types is the convolutional coding system .The Viterbi decoding algorithm is a maximum-likelihood decoding algorithm, which uses the remerging structure of a trellis of convolutional code to reduce the implementation complexity. This thesis provides design and computer simulation of both the convolutional encoding part and the Viterbi decoding method based on using the Artificial Neural Network. Artificial Neural Network is implementing the decoding part of convolutional code through different case studies that have been performed, to investigate the effect of the input message lengths, constraint length and the complexity of implementation. A comparison of the results obtained from Viterbi decoding method (based on ANN technique) with the results obtained from Viterbi decoding method (based on maximum likelihood ratio technique) was performed to investigate the performance of the using ANN technique in this application. The software implementation was simulated using programming facilities of (MA TLA B) package version 6. /.