The ongoing global pandemic of infection disease COVID-19 caused by the 2019 novel coronavirus (SARS-COV-2, formerly 2019-nCoV) presents critical threats to public health and the economy since it was identified in China, December 2019. The genome of SARS-CoV-2 had been sequenced and structurally annotated, yet little is known of the intrinsic organization and evolution of the genome. To this end, we present a mathematical method for the genomic spectrum, a kind of barcode, of SARS-CoV-2 and common human coronaviruses. The genomic spectrum is constructed according to the periodic distributions of nucleotides, and therefore reflects the unique characteristics of the genome. The results demonstrate that coronavirus SARS-CoV-2 exhibits dinucleotide TT islands in the non-structural proteins 3, 4, 5, and 6. Further analysis of the dinucleotide regions suggests that the dinucleotide repeats are increased during evolution and may confer the evolutionary fitness of the virus. The special dinucleotide regions in the SARS-CoV-2 genome identified in this study may become diagnostic and pharmaceutical targets in monitoring and curing the COVID-19 disease.