Infections with the influenza C virus causing respiratory symptoms are common, particularly among children. Since isolation and detection of the virus are rarely performed, compared with influenza A and B viruses, the small number of available sequences of the virus makes it difficult to analyze its evolutionary dynamics. Recently, we reported the full genome sequence of 102 strains of the virus. Here, we exploited the data to elucidate the evolutionary characteristics and phylodynamics of the virus compared with influenza A and B viruses. Along with our data, we obtained public sequence data of the hemagglutinin-esterase gene of the virus; the dataset consists of 218 unique sequences of the virus collected from 14 countries between 1947 and 2014. Informatics analyses revealed that (1) multiple lineages have been circulating globally; (2) there have been weak and infrequent selective bottlenecks; (3) the evolutionary rate is low because of weak positive selection and a low capability to induce mutations; and (4) there is no significant positive selection although a few mutations affecting its antigenicity have been induced. The unique evolutionary dynamics of the influenza C virus must be shaped by multiple factors, including virological, immunological, and epidemiological characteristics.