The International Maritime Organization (IMO) announced in April 2018 a target of cutting greenhouse gas (GHG) emissions from the sector by 50 percent below 2008 levels by 2050 and subsequent meetings of the IMO will develop a strategy for making headway on this commitment. This paper seeks to inform dialogue about the possibility of a carbon tax as a key element of GHG mitigation policy for international maritime transport. The paper discusses the case for the tax over alternative mitigation instruments, options for the practical design issues, and then presents estimates of the impacts of carbon taxation and other instruments from an analytical model of the maritime sector.