This paper quantifies the effects of a hypothetical $40 per ton of CO2 tax on maritime transport implemented worldwide. Calculations are based on trade data covering the 2012-2018 period for 185 countries and on a multisector structural gravity model designed to isolate seaborne trade and to incorporate marine fuel price in trade cost variables. We focus on the effects of the tax on 2018 trade flows at a disaggregated HS2 sector level. The counterfactual analysis estimates an average national purchasing power loss of 0.73% on tradables, corresponding to a global economic cost of 166 billion dollars. While OECD countries would lose on average 0.37% of purchasing power, Least Developed countries would lose on average 1.11% highlighting the inequitable distribution of effects. Such a tax, representing 29% of the baseline price, would reduce the emissions from maritime transport by approximately 1.75%, but its impact on global carbon emissions would be offset by the redirection of trade flows towards more carbon intensive transport modes such as air or road. Finally, the tax revenue is estimated in a range from 19.6 to 59.5 billion dollars, much lower than the economic cost resulting from the effects of the tax on trade.