Does trade and investment liberalisation increase the growth in sales of sugar-sweetened beverages (SSBs)? Here, for the first time to our knowledge, we test this hypothesis using a unique data source on SSB-specific trade flows. We test whether lower tariffs effectively increase imports of SSBs, and whether a higher level of imports increase sales of SSBs. Cross-national fixed effects models were used to evaluate the association between SSBs sales and trade liberalisation. SSBs per capita sales data were taken from EuroMonitor, covering 44 low- and middle-income countries from 2001 to 2014, SSBs import data were from TradeMap, Foreign Direct Investment data were from EuroMonitor, and data on applied tariffs on SSB from the World Trade Organisation tariffs database, all 2015 editions. The results show that higher tariffs on SSBs significantly decreased per capita SSB imports. Each one percent increase in tariffs was associated with a 2.9% (95% CI: 0.9%-5%) decrease in imports of SSBs. In turn, increased imports of SSBs were significantly associated with greater sales of SSBs per capita, with each 10 percent increase in imports (in US$) associated with a rise in sales of 0.36 L per person (95% CI: 0.08-0.68). Between 2001 and 2014, this amounted to 9.1 L greater sales per capita, about 40% of the overall rise seen in this period in LMICs. We observed that tariffs were inversely but not significantly associated with sales of SSBs. In conclusion, lower tariffs substantially increased imports of SSBs in LMICs, which translated into greater sales. These findings suggest that trade policies which lower tariff barriers to SSB imports can be expected to lead to increased imports and then increased sales of SSBs in LMICs, with adverse consequences for obesity and the diseases that result from it.