Dolphin morbillivirus (DMV) has been deemed as one of the most relevant threats for fin whales (Balaenoptera physalus) being responsible for a mortality outbreak in the Mediterranean Sea in the last years. Knowledge of the complete viral genome is essential to understand any structural changes that could modify virus pathogenesis and viral tissue tropism. We report the complete DMV sequence of N, P/V/C, M, F and H genes identified from a fin whale and the comparison of primary to quaternary structure of proteins between this fin whale strain and some of those isolated during the 1990-'92 and the 2006-'08 epidemics. Some relevant substitutions were detected, particularly Asn52Ser located on F protein and Ile21Thr on N protein. Comparing mutations found in the fin whale DMV with those occurring in viral strains of other cetacean species, some of them were proven to be the result of diversifying selection, thus allowing to speculate on their role in host adaptation and on the way they could affect the interaction between the viral attachment and fusion with the target host cells.