BackgroundSARS-CoV-2 is a new coronavirus that has spread globally, infecting more than 150000 people, and being declared pandemic by the WHO. We provide here bio-informatic, evolutionary analysis of 351 available sequences of its genome with the aim of mapping genome structural variations and the patterns of selection. MethodsA Maximum likelihood tree has been built and selective pressure has been investigated in order to find any mutation developed during the SARS-CoV-2 epidemic that could potentially affect clinical evolution of the infection. FindingWe have found in more recent isolates the presence of two mutations affecting the Non-Structural Protein 6 (NSP6) and the Open Reding Frame10 (ORF 10) adjacent regions. Amino acidic change stability analysis suggests both mutations could confer lower stability of the protein structures. InterpretationOne of the two mutations, likely developed within the genome during virus spread, could affect virus intracellular survival. Genome follow-up of SARS-CoV-2 spread is urgently needed in order to identify mutations that could significantly modify virus pathogenicity.