In recent years, a massive amount of genomic DNA sequences are being created which leads to the development of new storing and archiving methods. There is a major challenge to process, store or transmit the huge volume of DNA sequences data. To lessen the number of bits needed to store and transmit data, data compression (DC) techniques are proposed. Recently, DC becomes more popular, and large number of techniques is proposed with applications in several domains. In this paper, a lossless compression technique named Arithmetic coding is employed to compress DNA sequences. In order to validate the performance of the proposed model, the artificial genome dataset is used and the results are investigated interms of different evaluation parameters. Experiments were performed on artificial datasets and the compression performance of Arithmetic coding is compared to Huffman coding, LZW coding, and LZMA techniques. From simulation results, it is clear that the Arithmetic coding achieves significantly better compression with a compression ratio of 0.261 at the bit rate of 2.16 bpc.