Data compression is a size reduction of data to be sent via network or to be stored on auxiliary storage for long time, thus data compression will save storage capacity, speed up file transfer, speedup data transmission by decreasing transferring time, and decrease costs for storage hardware and network bandwidth. In this paper we will investigate Huffman and LZW methods of data compression-decompression. Different images in sizes and types will treated, compression, decompression times will be evaluated, compression ratio will obtained, the obtained results will be analyzed in order to do some judgments.