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Compression is very often considered as finding patterns in raw data that are amenable to more economical representation. However, it’s not often recognized that the problem of data compression can take different hues. Luckily Human Genome project was decoded and creates lot of challenges in the era of Genome (DNA) compression. Compressing Deoxyribonucleic acid (DNA) sequences is a very important task as on a daily basis thousands of gigabytes of sequences of nucleotides and amino acids gets archived in Genbank. Storing giant Genomes in a laptop computer within the compressed type is an economical means that of victimization Deoxyribonucleic acid sequences for biological functions. Today, a lot of and a lot of Deoxyribonucleic acid sequences are getting out there. The knowledge concerning Deoxyribonucleic acid sequences square measure hold on in biology databases. Need for Compression arises as a result of close to forty five billion bases in four corer living organisms within the GenBank database (http://www.ncbi.nlm.nih.gov/Genbank/) better compression may additionally reveal some inherent biological structures, abet in phylogenic tree reconstruction. To forecast the future needs the simulation results of different living organism’s records to be hold on. State of the art DNA compression algorithm results are limited to 1.6 bits per base (bpb). Exponential increase causes terribly onerous to obtain QOS in communication. In the present work an attempt is made to review the previous art of compression techniques with proposed model i.e. GreaM(Genome repetitive & Non-repetitive Encoding analysis model) through a mathematical comparative analysis and the proposed GreaM model is to be prove an a first art technique and invaluable tool in the Bio Informatics-era.